8^(3x-9)-12=500

Question

solving for x 

Answer 1

Arturo's method is absolutely correct in using logarithms

to solve this.  However, if you realize that 512 is a power

of 2, this can be done without logarithms:

 

8^3x-9 -12 = 500

8^3x-9 = 512

 

8 = 2³ and 512 = 2⁹ so:

 

2^3(3x-9)  = 2⁹

2^9x-27 = 2⁹

9x - 27 = 9

9x = 36

x=4

Answer 2

I assume the -12 is not part of the exponent.

 

8^3x-9 - 12 = 500

 

8^3x-9 = 512

 

(3x-9) log8 = log512

 

3x-9 = (log512 / log8)

 

x = (1/3) [(log512 / log8) + 9] = 4

 

Go ahead and substitute x = 4 into the original equation to test the solution.