Question

How do you rewrite ${\log _5}125 = 3$ in exponential form?

Answer 1

Hint: We solve the given equation using the identity formula of logarithm ${\log _e}a = x\,$which gets converted into $a = {e^x}$. We decide on the base of the logarithmic base. The base of $\ln $ in general cases is always $e$. The main step would be to eliminate the logarithm function and keep only the linear equation of x. We solve the linear equation with the help of basic binary operations.

Complete step-by-step solution:
We take the logarithmic identity for the given equation ${\log _5}125 = 3$ to rewrite in exponential form.
We have ${\log _5}125 = 3$.
We have a single equation of logarithm and a constant on the opposite sides of the equation.
Now we have to eliminate the logarithm function to find the exponential form.
We know ${\log _e}a = x\,$ gets converted into $a = {e^x}$. Applying the rule in case of ${\log _5}125 = 3$, we get,
$ \Rightarrow {5^3} = 125$

Therefore, the exponential form of ${\log _5}125 = 3$ is ${5^3} = 125$.

Note: The logarithm is used to convert a large or very small number into the understandable domain. For the theorem to work the usual conditions of logarithm will have to follow. In case of the base is not mentioned then the general solution for the base for logarithm is $10$. But the base of $e$ is fixed for $e$. We also need to remember that for logarithm function there has to be a domain constraint.