Question

Solve each exponential equation. Give the exact value for x.
(a) 5^x = 0.04

x =

(b) 7^x = 10

x =

(c) 8^x = 6.5

x =

(d) 4^x = 5

x =

Answer 1

I'll do one and then see if you can do the others:
We have to take the log of both sides and then use our log laws to rearrange for x to be the subject.

\[5^x=0.04\]
\[log(5^x)=log(0.04)\]
\[xlog(5)=log(0.04)\]
\[x=\frac{log(0.04)}{log(5)}\]

Does that make sense?

Answer 2

It does make sense and I appreciate your assistance. :)

Answer 3

You're welcome :P