
Math
To 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...

Math
`ln(4x7)=ln(x+11)` Using one to one property of logarithms, `4x7=x+11` `=>4xx=11+7` `=>3x=18` `=>x=18/3` `=>x=6` Plug back the solution in the equation to check the solution,...

Math
To solve the equation `log_5(5x+9)=log_5(6x)` , we apply logarithm property: `a^(log_a(x))=x` . Raise both sides by base of `5` . `5^( log_5(5x+9))=5^(log_5(6x))` `5x+9=6x` Subtract `5x` from...

Math
For the given equation `2^(0.1x)5=12` , we may simplify by combining like terms. Add `5` on both sides of the equation. `2^(0.1x)5+5=12+5` `2^(0.1x)=17` Take the "`ln` " on both sides to be able...

Math
For the given equation `0.5^x0.25=4` , we may simplify by combining like terms. Add `0.25` on both sides of the equation. `0.5^x0.25+0. 25=4+0.25` `0.5^x=4.25` Take the "`ln` " on both sides to...

Math
For the given equation `10^(3x)+4 =9` , we may simplify by combining like terms. Subtract 4 from both sides of the equation. `10^(3x)+44 =94` `10^(3x)=5` Take the "ln" on both sides to be able to...

Math
To solve the given equation `7^(6x)=12` , we may take "`ln` " on both sides of the equation. `ln(7^(6x))=ln(12)` Apply natural logarithm property: `n*ln (x)=ln (x^n)` . `6x*ln(7)=ln(12)` Divide...

Math
To solve the given equation `7^(3x)=18` , we may take "ln" on both sides of the equation. `ln(7^(3x))=ln(18)` Apply natural logarithm property:` ln (x^n) = n*ln (x)` . `3xln(7)=ln(18)` Divide both...

Math
To solve the given equation `8^x=20` , we may take "ln" on both sides of the equation. `ln(8^x)=ln(20)` Apply natural logarithm property: `ln (x^n) = n*ln (x)` . `xln(8)=ln(20)` Divide both sides...

Math
To evaluate the given equation `25^(10x+8)=(1/125)^(42x)` , we may apply `25=5^2` and `1/125=5^(3)` . The equation becomes: `(5^2)^(10x+8)=(5^(3))^(42x)` Apply Law of Exponents: `(x^n)^m =...

Math
To evaluate the given equation `10^(3x10)=(1/100)^(6x1)` , we may apply `100=10^2` . The equation becomes: `10^(3x10)=(1/10^2)^(6x1)` Apply Law of Exponents: `1/x^n = x^(n)` ....

Math
To evaluate the given equation `36^(5x+2)=(1/6)^(11x)` , we may apply `36=6^2` and `1/6=6^(1)` . The equation becomes: `(6^2)^(5x+2)=(6^(1))^(11x)` Apply Law of Exponents: `(x^n)^m = x^(n*m)`...

Math
`3^(3x7)=81^(123x)` To solve, factor 81. `3^(3x7)=(3^4)^(123x)` To simplify the right side, apply the exponent rule `(a^m)^n=a^(m*n)` . `3^(3x7)=3^(4*(123x))` `3^(3x7)= 3^(4812x)` Since...

Math
To evaluate the given equation `4^(2x5)=64^(3x)` , we may let `64 =4^3` . The equation becomes: `4^(2x5)=(4^3)^(3x)` . Apply Law of exponents: `(x^n)^m = x^(n*m)` . `4^(2x5)=4^(3*3x)`...

Math
`27^(4x1)=9^(3x+8)` To solve, factor the 9 and 27. `(3^3)^(4x1)=(3^2)^(3x+8)` To simplify each side, apply the exponent rule `(a^m)^n=a^(m*n)` . `3^(3*(4x1))=3^(2*(3x+8))` `3^(12x3)=3^(6x+16)`...

Math
`8^(x1)=32^(3x2)` To solve, factor 8 and 32. `(2^3)^(x1)=(2^5)^(3x2)` To simplify each side, apply the exponent rule `(a^m)^n = a^(m*n)` . `2^(3*(x1)) = 2^(5*(3x2))` `2^(3x3) = 2^(15x10)`...

Math
`7^(3x+4)=49^(2x+1)` To solve, factor the 49. `7^(3x+4)=(7^2)^(2x+1)` To simplify the right side, apply the exponent property `(a^m)^n=a^(m*n)` . `7^(3x+4)=7^(4x+2)` Since the two sides have the...

Math
`5^(x4)=25^(x6)` To solve, factor the 25. `5^(x4)=(5^2)^(x6)` To simplify the right side, apply the exponent rule `(a^m)^n = a^(m*n)` . `5^(x4)=5^(2*(x6))` `5^(x4)=5^(2x12)` Since both...

Math
To determine the power function `y=ax^b` from the given coordinates: `(5,10)` and `(12,81)` , we setup system of equations by plugin the values of x and y on `y=ax^b.` Using the coordinate...

Math
To determine the power function `y=ax^b` from the given coordinates: `(4,8) ` and `(8,30)` , we setup system of equations by plugin the values of `x` and `y` on `y=ax^b` . Using the coordinate...

Math
We are asked to write a power function whose graph includes the points (3,14) and (9,44): `14=a3^b,44=a9^b` From the first equation we get: `a=14/(3^b)` Then `44=(14/(3^b))*9^b` `44=14*3^b`...

Math
We are asked to write a power function whose graph includes the points (2,3) and (6,12). Substitute the given x,y values into the base equation to get two equations in the two unknowns a,b. Solve...

Math
We are asked to write a power function whose graph includes the points (5,9) and (8,34). Substitute the given x,y pairs into the base model to get two equations with the two unknowns a,b. Solve the...

Math
We are asked to write the equation for a power function whose graph passes through the points (4,3) and (8,15). We substitute the known values of x and y into the basic equation to get two...

Math
The given two points of the exponential function are (1,40) and (3,640). To determine the exponential function `y=ab^x` plugin the given x and y values. For the first point (1,40), plugin x=1...

Math
The given two points of the exponential function are (1,2) and (3,50). To determine the exponential function `y=ab^x` plugin the given x and y values. For the first point (1,2), plugin x=1 and...

Math
The given two points of the exponential function are (3,27) and (5,243). To determine the exponential function `y=ab^x` plugin the given x and y values. For the first point (3,27), the values of x...

Math
To determine the power function `y=ax^b` from the given coordinates: `(3,1)` and `(5,4)` , we setup system of equations by plugin the values of x and y on `y=ax^b` . Using the coordinate `(3,1)`...

Math
The given two points of the exponential function are (2,24) and (3,144). To determine the exponential function `y=ab^x` plugin the given x and y values. For the first point (2,24), the values of x...

Math
The given two points of the exponential function are (1,3) and (2,12). To determine the exponential function `y=ab^x` plugin the given x and y values. For the first point (1,3), plugin x = 1 and...

Math
We are asked to write the equation of the parabola with directrix x=1/18 and vertex at the origin: The equation for a parabola with vertex at the origin and focus (a,0) is `y^2=4ax ` Since the...

Math
We are asked to write the equation of the parabola with directrix y=5/12 and vertex at the origin: The equation for a parabola with vertex at the origin and focus (0,a) is `x^2=4ay ` Since the...

Math
We are asked to write the equation of the parabola with vertex at the origin and directrix x=11: The equation of a parabola with vertex at the origin and focus at (a,0) is `y^2=4ax ` ; the parabola...

Math
A parabola with directrix at` x=a` implies that the parabola may opens up sideways towards to the left or right. The position of the directrix with respect to the vertex point can be used to...

Math
A parabola with directrix at `y=k` implies that the parabola may opens up towards upward or downward direction. The position of the directrix with respect to the vertex point can be used to...

Math
A parabola with directrix at `y=k` implies that the parabola may open up towards upward or downward direction. The position of the directrix with respect to the vertex point can be used to...

Math
A parabola opens toward to the location of focus with respect to the vertex. When the vertex and focus has same yvalues, it implies that the parabola opens sideways (left or right). When the...

Math
A parabola opens toward to the location of focus with respect to the vertex. When the vertex and focus has same yvalues, it implies that the parabola opens sideways (left or right). When the...

Math
We are asked to write the equation of the parabola with focus (0,6) and the vertex at the origin: The equation for a parabola with focus (0,a) and vertex at the origin is `x^2=4ay ` The equation...

Math
We are asked to write the equation for the parabola with focus (0,8) and vertex at the origin: The equation for a parabola with focus (0,a) and vertex at the origin is `x^2=4ay ` So the equation we...

Math
We are asked to write the equation of the parabola with focus (3,0) and vertex at the origin. The formula for a parabola with focus (a,0) and vertex at the origin is ` y^2=4ax ` The equation...

Math
We are asked to write the equation of a parabola with focus at (2,0) and vertex at the origin. The equation for a parabola with focus at (a,0) and vertex at the origin is ` y^2=4ax ` The equation...

Math
Let `y^2=4px` be equation of parabola. Then equation of directrix is `x=p` coordinates of focus are `(p,0)` and axis of symmetry is `x`axis. In this case equation of parabola is `5x+1/3y^2=0`...

Math
Let `x^2=4py` be equation of parabola. Then equation of directrix is `y=p,`coordinates of focus are `(0,p)` and axis of symmetry is `y`axis. In this case the equation of parabola is...

Math
Let `y^2=4px` be equation of parabola. Then equation of directrix is `x=p ` coordinates of focus are `(p,0)`and axis of symmetry is `x`axis. In this case equation of parabola is `4x11y^2=0`...

Math
Let `x^2=4py` be equation of parabola. Then equation of directrix is `y=p` coordinates of focus are `(0,p)` and axis of symmetry is `y`axis. In this case the equation of parabola is...

Math
Let `y^2=4px` be equation of parabola. Then equation of directrix is `x=p` coordinates of focus are `(p,0)` and axis of symmetry is `x`axis. In this case equation of parabola is `14x=6y^2`...

Math
Let `y^2=4px` be equation of parabola. Then equation of directrix is `x=p` coordinates of focus are `(p,0)` and axis of symmetry is `x`axis. In this case equation of parabola is `24x=3y^2`...

Math
Let `y^2=4px` be equation of parabola. Then equation of directrix is `x=p` coordinates of focus are `(p,0)` and axis of symmetry is `x`axis. In this case equation of parabola is `y^2=18x`...

Math
Let `x^2=4px` be equation of parabola. Then equation of directrix is `y=p` coordinates of focus are `(0,p)` and axis of symmetry is `y`axis. In this case the equation of parabola is `5x^2=15y`...