Question

How do you solve `5^(3log_5 4)=x`?

Answer 1

Use properties of logarithms `(a)log(b) = log(b^a)` and `b^(log_b(f(x))) = f(x)`

Explanation:

Use the property of logarithms `(a)log(b) = log(b^a)`:

`x = 5^(log_5(4^3))`

A property of logarithms is, exponentiation of the base the logarithm are inverses, `b^(log_b(f(x))) = f(x)`:

`x = 4^3`

`x = 64`

Answer 2

`x=64`

Explanation:

As we have `5^(3log_5 4)=x` and as `nlog_a b=log_a b^n`

`5^(3log_5 4)=x` is equivalent `5^(log_5 4^3)=x`

or `5^(log_5 64)=x`

and from definition of log, we have

`log_5 x=log_5 64`

Hence `x=64`