Question

how do i solve for x?
25^(2x) = 125^(x+2)

Answer 1

\[25=5^{some power}\]
what is that power?

Answer 2

\[125=5^?\]
also want to write 125, as 5^?

Answer 3

So if we can write both sides having the same base, all we need to do is set the exponents equal

Answer 4

\[\text{ what is } 5^2?\]
\[\text{ what is } 5^3 ?\]

Answer 5

5^2 = 25
5^3 = 125

Answer 6

yeah so we can do the following :
\[(5^2)^{2x}=(5^3)^{x+2}\]

Answer 7

\[5^{2 \cdot 2x}=5^{3(x+2)}\]

Answer 8

so the bases are the same set the exponents equal to each other and solve for x

Answer 9

k, thanks

Answer 10

does x= 6

Answer 11

\[2 \cdot 2x=3(x+2)\]
\[4x=3x+6\]
\[4x-3x=6\]
\[1x=6 \]
\[x=6\]

Answer 12

yep