eNotes Homework Help is a way for educators to help students understand their school work. Our experts are here to answer your toughest academic questions! Once it’s posted to our site, your question could help thousands of other students.
Popular Titles

MathFor exponential equation: `5^(6x)= 8320` , we may apply the logarithm property: `log(x^y) = y * log (x).` This helps to bring down the exponent value. Taking "log" on both sides:...

MathProblem:` 3^(2x)=75` is an exponential equation. To simplify, we need to apply logarithm property: `log(x^y) = y*log(x)` to bring down the exponent that is in terms of x. Taking "log" on both...

Math`log_3(x) + log_3(x  2) = 1` The logarithms at the left side have the same base. So express the left side with one logarithm only using the rule `log_b (M) + log_b (N) = log_b(M*N` ). `log_3(x *...

Math`x^2x=log_5 (25)` First, simplify the right side of the equation. To do so, factor 25. `x^2  x = log_5 (5^2)` Then, apply the logarithm rule `log_b (a^m) = m * log_b (a)` . `x^2  x = 2 * log_5...

Math`log_b (27) = 3` To solve, convert this to exponential equation. Take note that if a logarithmic equation is in the form `y = log_b (x)` its equivalent exponential equation is: `x = b^y` So...

Math`log_3 (x) = 1` To solve, convert this to exponential equation. Take note that if a logarithmic equation is in the form `y = log_b (x)` its equivalent exponential equation is: `x = b^y` So...

Math`log_3(1/81) = x` To solve this, consider the base and argument of the logarithm. The base of the logarithm is 3. And the argument has 81 which is multiple of 3. Factoring 81, the equation...

Math`log_10 (1000) = x` To solve, express the 1000 in terms of 10. `log_10 (10 * 10 * 10)=x` `log_10 (10^3) =x` To simplify the left side, apply the logarithm rule `log_b (a^m) = m*log_b(a)` . `3*...

MathTake note that if a logarithmic equation is in the form `y = log_b (x)` its equivalent exponential equation is: `x = b^y` Thus, converting `log_3 (1/9) = 2` to exponential equation, it becomes...

MathTake note that if a logarithmic equation is in the form `y=log_b(x)` its equivalent exponential equation is `x=b^y` Thus, converting `log_10 (0.01) =2` to exponential equation, it becomes:...

MathTake note that if the exponential equation is in the form `y=b^x` its equivalent logarithmic form is `x=log_b (y)` Thus, converting `27^(2/3)=9` to logarithmic form, it becomes `2/3=log_27 (9)`

MathTake note that if an exponential equation is in the form `y = b^x` its equivalent logarithmic form is `x=log_b(y)` Thus, converting `2^3=8` to logarithmic form, it becomes: `log_2(8)=3`

Math`log_a (1/a)` To simplify this, apply the negative exponent rule for `1/a` . `=log_a (a^(1))` Then, apply the logarithmic rule `log_b(x^m)=m*log_b(x)` . `= 1 * log_a (a)` Take note that when the...

Math`log_7 (1)` Take note that if the argument of a logarithm is 1, its resulting value is zero `(log_b(1) = 0)` . `= 0` Therefore, `log_7 (1) = 0` .

Math`log_27 (9)` To evaluate, let this expression be equal to y. `y = log_27 (9)` Then, convert this equation to exponential form. Take note that if a logarithmic equation is in the form `y = log_b...

Math`log_2 (1/8)` To evaluate this, consider the base and argument of the logarithm. The base of the logarithm is 2. And the 8 can be expressed in terms of factor 2. So factoring 8, the expression...

ReferenceAmbiguity is created because the function of the word "visiting" is unclear in the sentence. The intended meaning depends on whether the word "visiting" is being used as a gerund (a verb...

I Know Why the Caged Bird SingsAfter recounting the past, Maya Angelou realizes she has the ability to thrive despite the insidious influence of racism and the dysfunction of her childhood. Maya comes to see her past experiences...

History“The Double Life of Pocahontas,” written by Jean Fritz, is a historical account of the life of the daughter of a Powhatan chief. For background information, Jean Fritz uses written accounts...

HistoryThe main idea of The War of 1812: A History from Beginning to End is that the War of 1812 had its roots in conflicts that went back to the previous century and that it was a farreaching conflict....

MacbethMacbeth is certainly the one who determines the course his life takes. The moment he decides to murder king Duncan is the moment he accepts evil. Once he does that, he cannot go back to the point...

Business

The Open WindowWhen determining author's purpose, think about the acronym P.I.E., which stands for "persuade, inform, entertain." A story's purpose can usually be understood from these three points. The purpose...

MacbethPrior to killing Duncan, Macbeth felt guilty and unsure. He told his wife, Lady Macbeth, "We will proceed no further in this business" (1.7.34), and he even hallucinates a dagger, first clean and...

The OdysseyIn The Odyssey, heroism is portrayed as something which men are capable of  Penelope is cunning and clever, but she is never discussed as heroic  and heroism is achievable by fighting external...

Romeo and JulietDoes the quote "a plague on both your houses" have any significance in the play of Romeo and Juliet?Mercutio utters this line  "A plague o' both your houses!"  after he has been killed by Tybalt. Tybalt came looking for Romeo in order to challenge him to a fight because he was offended by...

MathHello! It is obvious that there is no linear formula exactly connecting these x's and y's, if we consider the slopes between neighbor points: `(155  134)/(31  30) = 21,` `(165  155)/(33  31) =...

MacbethMacbeth is all about trust and betrayal. So, here are two major examples of the abuse of trust in the play. 1. At the beginning of the play, king Duncan strips the traitorous Thane of Cawdor of his...

MathHello! Suppose that the two numbers are both >=2 (if one of the numbers is 1, the problem is trivial). Then both have its unique decomposition into prime factors. If we find this decomposition,...

MathParent functions are the most basic, or "simplest" form of a given function with no transformations placed upon them. For example, `y=4x^2+2x+5` is a quadratic function. The parent is: `y=x^2` The...

MathAn operation follows the Commutative property if changing the order of the numbers in the operation does not change the outcome. Thus, addition (and multiplication) are commutative (i.e., a+b=b+a...

MathFor a stem and leaf plot, the number to the left of the bar is generally the stem and the numbers to the right of the bar are the leaves. The stem is the first digit(s) and the leaves are the next...

MathTo do this, the longest rod would be the diagonal of the box. Now, this is different than the diagonal of one side of the box. I am talking about the diagonal that would go through the middle of...

A Christmas CarolThe Ghost of Christmas Present says these words to Scrooge after he has shown Scrooge this Christmas at the Cratchit family's home. Scrooge has begun to soften, especially having seen Tiny Tim and...

Young Goodman BrownThe short answer is this: we don't know for sure. When Goodman Brown implores his wife, Faith, to "'Look up to Heaven, and resist the Wicked One!,'" he is snatched away from the scene. He finds...

LiteratureIn Chapter 1 of Hoot, Roy is riding the bus to school on a Monday morning. An older boy named Dana is bullying Roy by smashing his face against the bus window and squeezing Roy's head with his...

The Great GatsbyThis is ultimately a matter of personal opinion, but I believe that Gatsby was the instigator of his own tragic demise. Gatsby's motivations throughout the entirety of the book are hidden and...

Harrison BergeronKurt Vonnegut's short story "Harrison Bergeron" examines a futuristic world in which all people have been rendered equal through the use of personalized handicaps for those who excel at a...

Fever 1793Matilda "Mattie" Cook is a young girl living in Philadelphia with her mother and grandfather if 1793. In the first chapter, which takes place on August 16th, Mattie wakes up on a very hot morning...

SlaughterhouseFiveIn Chapter Five of Kurt Vonnegut's Slaughterhouse Five, Billy has a very strange morphine dream in which he sees a garden with giraffes wandering around on gravel paths in it. In this dream, Billy...

ReferenceFirstly, instead of relying on secondhand information, it might be helpful for you to look up statements that Donald Trump himself has made. From those quotes, you could  depending on your...

MathHello! There are several reasons for this. The main reason, as I think, is to teach schoolkids logical thinking. Mathematics, as the most exact science, requires definitions, proofs and exact...

MathWell, at some point, all subjects can be related. For instance, you could use math quite easily in social sciences, studying peoples and populations, for instance. The "variable" would be how you...

HistoryThe Boston Massacre really did not have a purpose. It was not something that the British set out to do. Instead, it happened spontaneously. To the extent that it had a purpose, its purpose was...

LiteratureWhen Montag meets with Faber and earns his trust, they begin to collaborate on a plan to upend the elements of society that have led them to that point. Faber is the more practical and cynical of...

The Thorn BirdsIs Luke O'Neill in the Thorn Birds more like Amir from The Kite Runner or Rasheed from A Thousand...Colleen McCullough's Thorn Birds highlights the story of the Cleary family over the course of 54 years, emphasizing the life of Meghann "Meggie" Cleary who lives at Drogheda, a sheep station in the...

ReferenceThabo Mbeki compares the work of political advancement to the Comrades Marathon, South Africa's annual race between the cities of Durban and Pietermaritzburg. It is also the world's oldest and...

ReferenceThe problem with this sentence is that it is unclear if I saw an animal ("her duck"), or if I saw her perform the action of ducking. Let's break each possibility down grammatically. The first...

ReferenceThe key word here is “visiting.” Is it used as a verb, or as an adjective? If “visiting” is used as a verb in combination with the helping verb “are,” then this use is considered a...

ReferenceThe key word here is the adjective “right.” Which one of its meanings is used in this instructional sentence? If “right” is used to mean “correct,” then this instruction could be...