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_{8}(2x - 6) = 2\\)
answerhow to enter your answer (opens in new window)
4 points
\\(x =\\)

Explanation:

Step1: Convert log to exponential form

Recall that if $\log_b(a) = c$, then $b^c = a$. For $\log_8(2x - 6) = 2$, we have $8^2 = 2x - 6$.

Step2: Calculate $8^2$ and solve for x

$8^2 = 64$, so the equation becomes $64 = 2x - 6$. Add 6 to both sides: $64 + 6 = 2x$, which simplifies to $70 = 2x$. Divide both sides by 2: $x = \frac{70}{2} = 35$.

Answer:

$x = 35$