What is the solution to the equation 9^(x+1) =27

ANSWER

EXPLANATION

The given exponential equation is

The greatest common factor of 9 and 27 is 3.

We rewrite the each side of the equation to base 3.

Since the bases are equal, we can equate the exponents.

Expand the parenthesis to get:

Group similar terms

For this case we must solve the following equation:

We rewrite:

Then the expression is:

Since the bases are the same, the two expressions are only equal if the exponents are also equal. So, we have:

We apply distributive property to the terms within parentheses:

Subtracting 2 on both sides of the equation:

Dividing between 2 on both sides of the equation: