Question

How do you solve `log_5 x^3=15`?

Answer 1

`x=5^5`

Explanation:

`log_5x^3=15` means `5^15=x^3`

As `(5^5)^3=5^15`

`x^3=(5^5)^3` i.e. `x^3-(5^5)^3=0`, which can be factorized as

`(x-5^5)(x^2+5^5x+(5^5)^2)=0`

i.e. `x=5^5`, if we consider the domain only as real numbers.

as `x^2+5^5x+(5^5)^2` is of the type `x^2+ax+a^2` and has complex roots because discriminant, which is `a^2-4a^2=-3a^2`, is always negative.