Question

Solve the equation
log3 (2x -5) =4 Remember to check your solution(s).
x=

Answer 1

To solve the equation \( \log_3(2x - 5) = 4 \), we will first rewrite the equation in exponential form.

The equation \( \log_b(a) = c \) can be rewritten as \( a = b^c \). Therefore, we can rewrite our equation as:

\[
2x - 5 = 3^4
\]

Calculating \( 3^4 \):

\[
3^4 = 81
\]

So we have:

\[
2x - 5 = 81
\]

Next, we can solve for \( x \) by first isolating \( 2x \):

\[
2x = 81 + 5
\]

\[
2x = 86
\]

Now, divide both sides by 2:

\[
x = \frac{86}{2} = 43
\]

Now, let's check the solution by substituting \( x = 43 \) back into the original equation:

\[
\log_3(2(43) - 5) = \log_3(86 - 5) = \log_3(81)
\]

Since \( 81 = 3^4 \), we know:

\[
\log_3(81) = 4
\]

This confirms that our solution is:

\[
\boxed{43}
\]