Question

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

Answer 1

`3^x=5`

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 √((3^x)^2)=√(25)`

`\implies 3^x=5`