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_{6}(2x - 6) = 2\\)\
answerhow to enter your answer (opens in new window)\
4 points

Explanation:

Step1: Convert to exponential form

Recall that if $\log_b(a) = c$, then $b^c = a$. For $\log_6(2x - 6) = 2$, we have $6^2 = 2x - 6$.

Step2: Simplify the exponential term

Calculate $6^2 = 36$, so the equation becomes $36 = 2x - 6$.

Step3: Solve for x

Add 6 to both sides: $36 + 6 = 2x$, which simplifies to $42 = 2x$. Then divide both sides by 2: $x=\frac{42}{2}=21$.

Answer:

21