How do I solve for x? (5)^2x=20

Question

tkhunny · Answer

1) Write very clearly what you mean.

$5^{2}\cdot x = 20$ or $5^{2x} = 20$?

anonymous · Answer

My apologizes; I don't know how to represent equations over the laptop, but it is indeed the second one you typed.

anonymous · Answer

$$5^{2x}=20$$

tkhunny · Answer

No worries.  Learning to communicate in this medium sometomes takes a little time.  I see you have almost figured it all out.  Good work.

Have you considered logarithms?

anonymous · Answer

How do logarithms come into play with this equation? -I mean that is the subject we are currently in, but I'm struggling with how they function in general. I find all this log/ln/natural base e stuff to be quite a mess.

tkhunny · Answer

Logarithms ARE exponents.
Logarithms are also useful for transforming expressions and saving relationships.

If $5^{2x} = 20$, then $\log\left(5^{2x}\right) = log(20)$

anonymous · Answer

I'm sorry, I don't know how to plug that into my calculator, is there a step process to solve that?

anonymous · Answer

1) In(25^x)=In(20)
2) x*In(25)=In(20)
then, x=In(20)/In(25)=0.9307

anonymous · Answer

I got that same number (0.9307) as well. Didn't seem right to me though; apparently it is! Thanks so much both of you.