What is the exponent rule of logarithms?

1 Answer
Sep 16, 2016

log_(a)(m^(n)) = n log_(a)(m)

Explanation:

Consider the logarithmic number log_(a)(m) = x:

log_(a)(m) = x

Using the laws of logarithms:

=> m = a^(x)

Let's raise both sides of the equation to nth power:

=> m^(n) = (a^(x))^(n)

Using the laws of exponents:

=> m^(n) = a^(xn)

Let's separate xn from a:

=> log_(a)(m^(n)) = xn

Now, we know that log_(a)(m) = x.

Let's substitute this in for x:

=> log_(a)(m^(n)) = n log_(a)(m)