Question

If 9^x=25, what does 3^x equal?

Answer 1

Answer:

$3^x=5$

Step-by-step explanation:

Given:

$9^x=25$

Rewrite 9 as 3²:

$\implies (3^2)^x=25$

$\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\implies 3^{2x}=25$

Apply the same exponent rule:

$\implies (3^x)^2=25$

Square root both sides:

$\implies \sqrt{(3^x)^2}=\sqrt{25}$

$\implies 3^x=5$