
LiteratureThe short answer is that the characters in Vonnegut's story find themselves in a situation very similar to the one described in Plato's scenario. They are prisoners in a carefully restricted,...

Law and PoliticsGenerally speaking, the government of a nation has the power to declare war. Typically, the constitution or other establishing laws of a nation will specify which part of the government can declare...

HistoryThe seven wonders of the ancient world include the following: the Pyramids of Giza, the Hanging Gardens of Babylon, the Temple of Artemis at Ephesus, the Statue of Zeus in Greece, the Mausoleum...

HamletHamlet opens with an atmosphere of of gloom and foreboding. Not only has King Hamlet, Hamlet's father, died recently, the guards on duty at the castle are discussing disquieting events with...

HistoryJohn Hancock was the first person to sign the Declaration of Independence. Hancock was the President of the Second Continental Congress, a meeting of delegates from the Thirteen Colonies, which...

BusinessA market economy is one in which the prices of goods, investments, and services are unimpeded by government regulation of any sort with the market and laws of supply and demand setting prices. The...

ScienceIt is important to make sure that when conducting a controlled experiment to test an hypothesis, all the variables are the same in two test groups except for the independent variable. In a...

Social SciencesThe important context for thinking about this is salary levels. Teachers are paid substantially less than other professionals with similar levels of education. They also tend to work high levels of...

ScienceThis might seem like something from a science fiction story. But there is actually strong evidence that plants respond to sound. In one intriguing study, researchers recorded the sound of a...

ScienceThere seems to be little consensus among the scientific community regarding the subject of birth order. Some experts believe that birth order merely decides personalities while others believe that...

ScienceThe term "sleep cycle" refers to the sequence of stages we pass through as we sleep. Typically, a sleeper repeats the cycle several times each night. Sleep cycles have been observed in many species...

LiteratureA work of literature is considered "a classic" if it has lasted through the proverbial test of time; that is, if it has an appeal that is enduring and it speaks in an universal manner to the human...

MacbethWhen Shakespeare's Macbeth begins, Macbeth is a noble and courageous military leader. He's defeated the King of Norway and the treacherous Macdonwald in a decisive battle, and for his efforts he is...

Law and PoliticsInteresting question! Over the years, many conspiracy theorists have hypothesized that the eye and pyramid represent the preeminent symbols of the Illuminati. The Illuminati is said to be a secret...

The ShiningYour first step in approaching this assignment should be to think about a particular stance and theoretical approach. Your introductory section should set out how you will approach the work. You...

HistoryMass incarceration is the imprisonment of an historically large proportion of Americans. Today, 5% of the population is in jail, which is five times the proportion of Americans who were in prison...

HistoryThe subject of Pagden's Peoples and Empires is the way European empires developed throughout history, starting in ancient Greece with Alexander the Great. Pagden defines empires as "government over...

Math`log_4(128)` To evaluate, factor 128. `= log_4 (2^7)` Then, apply the formula of change base `log_b (a) = (log_c (a))/(log_c (b))` . `= (log_2 (2^7))/(log_2 (4))` `= (log_2 (2^7))/(log_2 (2^2))` To...

Math`log_125 (625)` To evaluate, factor 625. `=log_125 (5^4)` Then, apply the formula of change base `log_b(a) = (log_c(a))/(log_c(b))` . `= (log_5 (5^4))/(log_5 (125))` `= (log_5 (5^4))/(log_5...

Math`log_8 (32)` To evaluate, factor 32. `=log_8 (2^5)` Then, apply the formula of change base `log_b(a) = (log_c(a))/(log_c(b))` . `= (log_2 (2^5))/(log_2 (8))` `=(log_2(2^5))/(log_2(2^3))` Also,...

Math`log_27 (9)` To evaluate, factor the 9. `= log_27 (3^2)` Then, apply the formula of change base `log_b (a) =(log_c(a))/(log_c(b))` . `= (log_3(3^2))/(log_3 (27))` `=(log_3 (3^2))/(log_3 (3^3))` To...

MathWe are asked to graph the following function: `y=log_5(x+1)3` The base function is `y=log_5(x)` and the graph will be a translation of 1 unit left and 3 units down of the graph of the base...

MathWe are asked to graph the function `y=log_6(x4)+2 ` : The graph is a translation of the graph of `y=log_6x ` 4 units right and 2 units up. The domain is x>4 and the range is all real numbers....

MathWe are asked to graph the function `y=log_4(x+2)1 ` : This is a translation of the graph of ` y=log_4x ` 2units left and 1 unit down. The domain is x>2 and the range is all real numbers. There...

MathWe are asked to graph the function `y=log_3x+4 ` : The graph is a translation of the graph `y=log_3x ` up 4 units. Some points on the graph: (1/27,1),(1/9,2),(1/3,3),(1,4),(3,5),(9,6) The domain is...

MathWe are asked to graph the function `y=log_2(x3) ` : The graph is a translation of the graph of `y=log_2x ` 3 units right. Some points on the graph:...

MathWe are asked to graph the following function: `y=log_(1/5)(x)` The domain is x>0 and the range is all real numbers. The graph is decreasing and concave up on the domain. Some points on the...

MathWe are asked to graph the following function: `y=log_(1/3)(x)` The domain is x>0 and the range is all real numbers. The graph of the function is decreasing and concave up on its domain. Some...

MathWe are asked to graph the following function: `y=log_6(x)` The domain is x>0 and the range is all real numbers. The graph is increasing on the domain, and the graph is concave down on the...

MathWe are asked to graph the following function: `y=log_4(x)` The domain is x>0 and the range is all real numbers. The graph increases on its domain and is concave down on its domain. Some points...

Math`2(log_3 (20)  log_3 (4)) + 0.5log_3(4)` First, apply the differencequotient rule of logarithm `log_b (m/n) = log_b(m)  log_b(n)` . `= 2 (log_3 (20/4))+0.5log_3(4)` `=2log_3(5) + 0.5log_3(4)`...

Math`ln40+2ln(1/2) + lnx` First, apply the logarithm rule `log_b (a^m)=m*log_b(a)` . `= ln40 + ln(1/2)^2 + ln x` `=ln40+ ln(1/4) + lnx` And, apply the rule `log_b(m*n) = log_bm +log_b n` . `= ln (40 *...

Math`5log_4(2) + 7log_4(x) + 4log_4(y)` To express this as one logarithm, first apply the rule `log_b a^m = m*log_b(a)` . `= log_4(2^5) + log_4(x^7) + log_4(y^4)` `= log_4(32) + log_4(x^7)+log_4(y^4)`...

MathWe are asked to solve `5^(2x)+20*5^x125=0 ` : Rewrite as ` (5^x)^2+20*5^x125=0 ` and let `y=5^x ` to get ` y^2+20y125=0` and (y+25)(y5)=0 so y=25 or y=5. y cannot be 25 as `5^x>0 ` for all...

MathWe are asked to solve `2^(2x)12*2^x+32=0 ` : Rewrite as `(2^x)^212*2^x+32=0 ` and let `y=2^x ` ; then `y^212y+32=0 ` and (y8)(y4)=0 so y=8 or y=4. y=8 ==> ` 2^x=8 ==> x=3 ` y=4 ==>...

MathTo solve the equation log_3(x)=log_9(6x), we may apply logarithm properties. Apply the logarithm property: `log_a(b)= (log_c(b))/log_c(a)` on `log_3(x)` , we get: `(log_9(x))/(log_9(3))=log_9(6x)`...

MathSolve `log_2(x+1)=log_8(3x) ` : Rewrite using the change of base formula: `(ln(x+1))/(ln(2))=(ln(3x))/(ln(8)) ` `(ln(8))/(ln(2))=(ln(3x))/(ln(x+1)) ` But `ln(8)=ln(2^3)=3ln(2) ` so:...

MathTo solve the equation: `10^(3x8)=2^(5x)` , we may take "ln" on both sides. `ln(10^(3x8))=ln(2^(5x))` Apply natural logarithm property: `ln(x^n) = n*ln(x)` . `(3x8)ln(10)=(5x)ln(2)` Let...

MathRewrite `6^(2x5)' as `(2 times 3)^(2x5) = 3^(2x5)2^(2x5)' Divide both sides of the equation through by `3^(x+4)' giving `1 = 3^(2x5x4)2^(2x5)' That is, `3^(x9)2^(2x5) = 1' Take logs (with...

MathTo evaluate the given equation `log_6(3x)+log_6(x1)=3` , we may apply the logarithm property: `log_b(x)+log_b(y)=log_b(x*y)` . `log_6(3x)+log_6(x1)=3` `log_6(3x*(x1))=3` `log_6(3x^23x)=3` To...

MathWe are asked to solve the following equation: `4ln(x)+3=21` Use basic algebraic rules to isolate the term with the logarithm: `4ln(x)=18` `ln(x)=9/2` Exponentiate both sides with base e:...

MathTo evaluate the given equation `log_4(x)+log_4(x+10)=2` , we may apply the logarithm property: `log_b(x)+log_b(y)=log_b(x*y)` . `log_4(x)+log_4(x+10)=2` `log_4((x)*(x+10))=2`...

MathTo evaluate the given equation `log_2(x4)=6` , we may apply the logarithm property: `a^(log_a(x))=x` . Raised both sides by base of `2` . `2^(log_2(x4))=2^6` `x4=64` Add `4` on both sides to...

MathTo evaluate the given equation `1/3log_5(12x)=2` , we may apply logarithm property: `n* log_b(x) = log_b(x^n)` . `log_5((12x)^(1/3))=2` Take the "log" on both sides to be able to apply the...

MathWe are asked to solve `log_8(512x)=log_8(6x1)` Exponentiating both sides with base 8 we get: 512x=6x118x=6 x=1/3. This is in the domain of both expressions of the equality (the domain for the...

MathTo evaluate the equation `log_6(3x10)=log_6(145x)` , we apply logarithm property: `a^(log_a(x))=x` . Raised both sides by base of `6` . `6^(log_6(3x10))=6^(log_6(145x))` `3x10=145x` Add `10`...

MathTo solve the equation `log_3(18x+7)=log_3(3x+38)` , we apply logarithm property: `a^(log_a(x))=x` . Raised both sides by base of `3` . `3^(log_3(18x+7))=3^(log_3(3x+38))` `18x+7=3x+38` Subtract 7...

Math`log(12x11)=log(3x+13)` Using the property of logarithmic equality, `12x11=3x+13` `=>12x3x=13+11` `=>9x=24` `=>x=24/9` `=>x=8/3` Let's plug back the solution in the equation to check...

Math`log_5(2x7)=log_5(3x9)` Using one to one property of logarithms, `2x7=3x9` `=>2x3x=9+7` `=>x=2` `=>x=2` Let's plug back the solution in the equation, `log_5(2*27)=log_5(3*29)`...

MathTo evaluate the equation `ln(x+19)=ln(7x8)` , we apply natural logarithm property: `e^(ln(x))=x` . Raise both sides by base of `e` . `e^(ln(x+19))=e^(ln(7x8))` `x+19=7x8` Subtract `7x` from both...
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