#1**0 **

Solve for x:

(log(x^2 - 4 x))/(log(9)) = (log(3 x - 10))/(log(9))

Subtract (log(3 x - 10))/(log(9)) from both sides:

(log(x^2 - 4 x))/(log(9)) - (log(3 x - 10))/(log(9)) = 0

Bring (log(x^2 - 4 x))/(log(9)) - (log(3 x - 10))/(log(9)) together using the common denominator log(9):

-(log(3 x - 10) - log(x^2 - 4 x))/(log(9)) = 0

Multiply both sides by -log(9):

log(3 x - 10) - log(x^2 - 4 x) = 0

log(3 x - 10) - log(x^2 - 4 x) = log(3 x - 10) + log(1/(x^2 - 4 x)) = log((3 x - 10)/(x^2 - 4 x)):

log((3 x - 10)/(x^2 - 4 x)) = 0

Cancel logarithms by taking exp of both sides:

(3 x - 10)/(x^2 - 4 x) = 1

Multiply both sides by x^2 - 4 x:

3 x - 10 = x^2 - 4 x

Subtract x^2 - 4 x from both sides:

-x^2 + 7 x - 10 = 0

The left hand side factors into a product with three terms:

-(x - 5) (x - 2) = 0

Multiply both sides by -1:

(x - 5) (x - 2) = 0

Split into two equations:

x - 5 = 0 or x - 2 = 0

Add 5 to both sides:

x = 5 or x - 2 = 0

Add 2 to both sides:

**Answer: x = 5 or x = 2(assuming a complex-valued log)**

Guest Feb 27, 2017

#2**0 **

Since the log bases are the same, we can forget the log part and solve this :

x^2 - 4x = 3x - 10 subtract 3x from both sides....add 10 to both sides

x^2 - 4x - 3x + 10 = 0

x^2 - 7x + 10 = 0 factor

(x - 5) (x - 2) = 0

Set both factors to = 0 and x = 5 or x = 2

However.....we must reject 2 because it makes both logs undefined.....so.....

x = 5 is the solution

CPhill
Feb 27, 2017