Question

In the equation 9^2 x 27^3 = 3^x, what is the value of x?
Show your work on scratchpaper

Answer 1

x=13

Explanation:

9^2 * 27^3 = 3^x

We need to get each term with a base of 3

9^2 = (3^2) ^2

We know that a^b^c = a^(b*c)

(3^2) ^2 = 3^(2+2) = 3^4

27^3 = (3^3) ^3 = 3^(3*3) = 3^9

Replacing these in the original equation

3^4 * 3^9 = 3^x

We know that a^b *a^c = a^(b+c)

3^4 * 3^9 =3^(4+9) = 3^13 = 3^x

The bases are the same, so the exponents must be the same

x=13