Question

solve 25^(x+2)=125^(x)

Answer 1

write 125 as a power of 25

Answer 2

\[\large 25=5^2 \\ \large 125=5^3\]

Answer 3

\[
25^{x+2}=125^x\\
25^{x+2}=(25^{3/2})^x\\
25^{x+2}=25^{3x/2}\\
x+2=3x/2
\]Can you solve from there?

Answer 4

lol I mean power of 5

Answer 5

I guess both work :P

Answer 6

Yep, both work. Writing as a power of five will be easier for you if you are not yet familiar with fractions as exponents.

Answer 7

nbouscal. is it solving like a regular equation after that?

Answer 8

Yep.

Answer 9

one minute.

Answer 10

is it x=1?
2=1.5-x
2=.5x
1=x

Answer 11

No.\[
x+2=\frac{3x}2\\
2(x+2)=3x
\]

Answer 12

so x=4 (after dispersing the 2)
2x+4=3x
4=x

Answer 13

Right. You can plug that back in and check to see that it's right. Use your calculator, you'll see that \(25^6=125^4.\)

Answer 14

yay!!! Thank you!!!!