Question

Can someone help me solve for x: 8^(x+2) = 32, please? Thank you.

Answer 1

I hope I can help. I got to the answer of x by using natural logs (ln). Specifically, the following is how I arrived at the answer:

8^(x+2)=32
(8^x)(8^2)=32 This simplifies the equation
ln[(8^x)(8^2)]=ln32
ln8^x+ln8^2=ln32
xln8+2ln8=ln32
The above follow the rules of natural logs
x(2.0794)+2(2.0794)=3.4657 These values came from a log table
2.0794x+4.1588=3.4657
2.0794x=3.4657-4.1588
2.0794x=-0.6931
x=-0.6931/2.0794
x=-0.333317=-0.3333

To verify this answer you can substitute this value into the original equation and you get the following:

8^(-0.3333+2)=8^1.6667=32.0022=32