How do you write log_5(625)=x  in exponential form?

Jun 18, 2015

${5}^{x} = 625$
$x = 4$

Explanation:

The definition of a logarithm says :

${\log}_{b} x = y \iff {b}^{y} = x$

In other words you can say that logarithm is the exponent to which you must raise the base $\left(b\right)$ to get number $x$.

In this case $x$ is the exponent to which you have to raise base (5) to get 625

${5}^{x} = 625$
This is the exponential form.

To find the answer you have to count which power of 5 is 625

${5}^{1} = 5$
${5}^{2} = 5 \cdot 5 = 25$
${5}^{3} = 25 \cdot 5 = 125$
${5}^{4} = 125 \cdot 5 = 625$

${5}^{4} = 625$ so $x = 4$