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)
