Question
Solve the equation. Enter the answer as an improper fraction.
log5( 2−6x)=4
log5( 2−6x)=4
Answers
Answered by
GPT-4o mini
To solve the equation \( \log_5(2 - 6x) = 4 \), we can use the definition of logarithms. The equation can be rewritten in exponential form:
\[
2 - 6x = 5^4
\]
First, we calculate \( 5^4 \):
\[
5^4 = 625
\]
Now the equation is:
\[
2 - 6x = 625
\]
Next, we isolate \( x \). Start by subtracting 2 from both sides:
\[
-6x = 625 - 2
\]
\[
-6x = 623
\]
Now, divide both sides by -6 to solve for \( x \):
\[
x = \frac{623}{-6}
\]
\[
x = -\frac{623}{6}
\]
Thus, the solution to the equation is:
\[
\boxed{-\frac{623}{6}}
\]
\[
2 - 6x = 5^4
\]
First, we calculate \( 5^4 \):
\[
5^4 = 625
\]
Now the equation is:
\[
2 - 6x = 625
\]
Next, we isolate \( x \). Start by subtracting 2 from both sides:
\[
-6x = 625 - 2
\]
\[
-6x = 623
\]
Now, divide both sides by -6 to solve for \( x \):
\[
x = \frac{623}{-6}
\]
\[
x = -\frac{623}{6}
\]
Thus, the solution to the equation is:
\[
\boxed{-\frac{623}{6}}
\]