Question

I can't seem to figure out what numbers to use to solve this equation.

Answer 1

Hello!

The first thing you should notice is that the exponent will be less than 1, as raising 27 to any power greater than 1 will make it larger, and you're trying to figure out what makes it equal to 3, a number less than 27.

Raising a number to a fractional power is taking its nth root: $21^{1/3}$ is $\sqrt[3]{21}$, so you'll really need to take the nth root of 27 to get 3. To figure out which root, write the number in exponential form with a base of 3:

$27^{x}$ = 3
$3^{3x}$ = $3^{1}$

Now, the bases are the same (they are both 3), so you can set the exponents equal to each other:

3x = 1

Divide both sides by 3 and you've isolated x:

$x = \frac{1}{3}$

Answer:
$27^{1/3} = 3$