Question

Solve. 1/25 = 5^(x + 4)

a. x = –7/2
b. x = –6
c. x = 9/2
d. x = 2

Answer 1

For this one, you need to convert (1/25) to an exponent with base 5

Answer 2

How do I do that?

Answer 3

1/25 = 1/(5^2) right?

Answer 4

When the exponent is also located in the denominator, you can switch the term to the numerator and give the exponent a negative sign.

So 1/25 = 1/(5^2) = 5^-2

Try to plug these into a calculator; they all yield the same result.

Answer 5

I still don't get it. Sorry :/
my teachers don't know how to teach.

Answer 6

That's ok! :) we're here to help! :)

Answer 7

A negative exponent is the same as having 1/something to the positive exponent.

Ex) 4^-2 is equivalent to 1/(4^2)

does that make sense?

Answer 8

\[b^{-n}=\frac{1}{b^n}\]
\[\frac{1}{25}=\frac{1}{5^2}=5^{-2}\]

Answer 9

So which answer is it?

Answer 10

If you can use what we've shown you, we can confirm it :) we're here to help you learn, not just give you the answers. I know it's hard sometimes, but if you learn it now, you won't have to worry about it later :)

Answer 11

C?

Answer 12

Are you just guessing?

Answer 13

\[5^{-2}=5^{x+4}\implies -2=x+4\]
\[-2=x+4\]
\[x=-6\]

Answer 14

Nope. And thank you!

Answer 15

*sigh* satellite73 is correct