Question

solve for z.
3^z = 81
z = \square
submit

Explanation:

Step1: Express 81 as a power of 3

We know that \( 3\times3\times3\times3 = 81 \), which can be written as \( 3^4 = 81 \).

Step2: Equate the exponents

Given the equation \( 3^z = 81 \), and we just found that \( 81 = 3^4 \), so the equation becomes \( 3^z = 3^4 \). Since the bases are the same and the exponential function is one - to - one, we can set the exponents equal to each other. That is, \( z = 4 \).

Answer:

\( 4 \)