Question

Solve the equation 2^(5x+1) = 8^(x-2)

Answer 1

8=2^3
2^(5x+1)=2^3^(x-2)
2^(5x+1)=2^[3(x-2)]
5x+1=3(x-2)

Answer 2

if you need to show intermediate step between 2^(5x+1)=2^[3(x-2)], take log_2 of each side
\[\log_{2}2^{5x+1}=\log_{2}2^{3(x-2)}\]
\[(5x+1)\log_{2}2=[3(x-2)]\log_{2}2\]
\[\log_{2}2=1\]
\[5x+1=3(x-2)\]

Answer 3

This was very helpful. Thank you very much!

Answer 4

yw