Question

Solve the equation. Enter the answer as an improper fraction.

log5(2−6x)=4


(1 point)
x=

Answer 1

To solve the equation \( \log_5(2 - 6x) = 4 \), we can rewrite it in exponential form. The equation states that \( 2 - 6x \) is equal to \( 5^4 \).

1. Convert the logarithmic equation to its exponential form:
\[
2 - 6x = 5^4
\]

2. Calculate \( 5^4 \):
\[
5^4 = 625
\]

3. Substitute \( 625 \) back into the equation:
\[
2 - 6x = 625
\]

4. Now, isolate \( x \) by first subtracting \( 2 \) from both sides:
\[
-6x = 625 - 2
\]
\[
-6x = 623
\]

5. Now divide both sides by \( -6 \):
\[
x = \frac{623}{-6}
\]
\[
x = -\frac{623}{6}
\]

The solution is:
\[
\boxed{-\frac{623}{6}}
\]