How to answer with using log? 4^(10-2x)=4096

Question

Anybody know how to solve this problem? 

 

Answer: 5-log4096/2log4

Answer 1

4^(10-2x)=4096

log4^(10-2x)=log4096

log(2^2)^(10-2x)=log2^12

log2^(20-4x)=log2^12

because you have log2 on both sides set the exponents equal to each other

20-4x=12

20-12=4x

8=4x

x=2

check: 4^6=4096

         4096=4096