82.7k views
0 votes
I can't seem to figure out what numbers to use to solve this equation.

I can't seem to figure out what numbers to use to solve this equation.-example-1
User Viktorzeid
by
8.6k points

1 Answer

2 votes
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
User David Robinson
by
7.7k points

No related questions found