Question

solve the following logarithmic equation, using a calculator if necessary to evaluate the logarithm. write your answer as a fraction or round your answer to two decimal places. \\(\log_{3}(2x - 1) = 3\\)

Explanation:

Step1: Convert log to exponential

Using the definition of logarithms: if $\log_b(a) = c$, then $b^c = a$. So for $\log_3(2x - 1) = 3$, we get $3^3 = 2x - 1$.

Step2: Calculate $3^3$

$3^3 = 27$, so the equation becomes $27 = 2x - 1$.

Step3: Solve for x

Add 1 to both sides: $27 + 1 = 2x$, so $28 = 2x$. Then divide both sides by 2: $x = \frac{28}{2} = 14$.

Answer:

14