The given equation is:

$4 = \log_3(2x - 1)$

Step 1: Convert logarithmic to exponential form

The general logarithmic equation $\log_a b = c$ can be rewritten as: $b = a^c$

Here, $a = 3$, $b = 2x - 1$, and $c = 4$. Thus: $2x - 1 = 3^4$

Step 2: Solve for $2x - 1$

$3^4 = 81$ So: $2x - 1 = 81$

Step 3: Solve for $x$

Add 1 to both sides: $2x = 82$

Divide by 2: $x = 41$

Final Solution:

$x = 41$

Would you like more details or have further questions? Here are related topics for deeper understanding:

1. How to convert logarithmic equations to exponential form.
2. The properties of logarithms in different bases.
3. Solving equations involving multiple logarithmic terms.
4. Graphing $y = \log_3(x)$ and understanding transformations.
5. Applications of logarithms in real-world problems.

Tip: Always check the domain of a logarithmic equation; ensure the argument (inside the log) is positive.