Solve the equation

Question

Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

 

log₇(x − 32) = log₇(9x)

 

x=?

Answer 1

Since the logs on both sides are the same base (i.e. 7),  Both sides can be exponentiated with 7 to get

 

x - 32  =  9x

 

The solution to this equation is  x =  -4.    However, since log₇(-36) is not defined, this is not a solution to the original equation.

 

Consequently,  there is NO SOLUTION