Question

"Solve for x (where log_x() denotes the logarithm on base x): log_x(25) = 2.50, x = __"

Answer 1

9514 1404 393

Answer:

x = 625^(1/5) ≈ 3.62390

Explanation:

Using the change of base formula, we have ...

`\log_x(25)=2.5\\\\(\log(25))/(\log(x))=2.5\\\\\log(x)=(\log(25))/(2.5)=0.4\log(25)=\log(25^(0.4))\\\\x=25^(0.4)=\sqrt[5]{25^2}=\boxed{\sqrt[5]{625}\approx 3.62390}`