Question

Solve 25^x = 5^(x^2-3) for x

Answer 1

\[25^{x}=5^{x^{2}-3}\]
Solve for x

Answer 2

25 = 5^2

Answer 3

so we can say

\[\large 25^{x}=5^{x^{2}-3}\]

\[\large (5^2)^{x}=5^{x^{2}-3}\]

\[\large 5^{2x}=5^{x^{2}-3}\]

and because the bases are equal, the exponents are equal, meaning that

\[\large 2x = x^2 - 3\]

Answer 4

do you see what to do from here?

Answer 5

Yes thank you.

Answer 6

ok great, yw