Write the equation in its equivalent exponential form. Then solve for x.

Question

log Subscript 3 Baseline left parenthesis x minus 2 right parenthesis equals 4
Question content area bottom
Part 1
log Subscript 3 Baseline left parenthesis x minus 2 right parenthesis equals 4 in its equivalent exponential form is
  
enter your response here. ​(Do not​ simplify.)

Answer 1

To rewrite the logarithmic equation \( \log_3 (x - 2) = 4 \) in its equivalent exponential form, we use the definition of a logarithm. The expression can be rewritten as:

\[ x - 2 = 3^4 \]

Next, we need to solve for \( x \):

1. Calculate \( 3^4 \): \[ 3^4 = 81 \]

2. Now substitute this value back into the equation: \[ x - 2 = 81 \]

3. Solve for \( x \) by adding 2 to both sides: \[ x = 81 + 2 \] \[ x = 83 \]

Thus, the solution for \( x \) is \( x = 83 \).

To summarize:

• The equivalent exponential form is \( x - 2 = 3^4 \).
• The value of \( x \) is \( 83 \).