4^2x+5 = 8^3x

Question

solve for x and im completely lost as to what to do.

Answer 1

Change to base 2: 2^(4x+10) = 2^(9x), since 4 = 2^2, and 8 = 2^3.

4x+10 = 9x

x = 2 <==Answer

Answer 2

Jess another slightly different way to solve this is to take logs of both sides of the equation giving

(2x+5)log4 = 3xlog8 rearranging gives

2x + 5=3x (log8/log4) now you can use your calculator to look up the logs or remember that the log of 4 base 2 is 2 and log8 base 2 is 3 so now we have

2x + 5 = 3x(3/2) or

(9/2)x - (4/2)x = 5 which is the same as 

(5/2)x = 5 or x = 2 QED

Good luck