Solve for x in an equation with an exponent

Published on October 28, 2024

Algebra

The solution to the equation (1/3)^(x+3) = 9^x is x = -1.

Question

Answer

The problem is:

Let’s solve this step-by-step.

1. Express both sides of the equation with the same base.

Notice that both 3 and 9 can be expressed as powers of 3:

$ \frac{1}{3} = 3^{-1}$

Substitute these into the equation:

2. Simplify using exponent rules.

Recall that

. Applying this rule:

3. Solve for x.

Since the bases are now the same, we can equate the exponents:

Simplify and solve for

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