Question: Question 15 (2 points) Solve for x. \[ 3^x = \frac{1}{81} \] Options: - x = -4 - x = 4 - x =…

Question 15 (2 points)

Solve for x.

\[ 3^x = \frac{1}{81} \]

Options:

• x = -4
• x = 4
• x = 4.33
• x = 0.25

Solution

Step 1: Rewrite \( \frac{1}{81} \) as a power of 3. \[ \frac{1}{81} = 3^{-4} & \] Step 2: Since the bases are the same, set the exponents equal. \[ x = -4 & \] x = -4