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 = (1)/(3)`

Answer:

`27^(1/3) = 3`