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 =

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 =

anonymous · Answer

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?

anonymous · Answer

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

anonymous · Answer

You're welcome :P