which of the following is equivalent to \\(\\frac{\\log(t)}{\\log_{8}(t)}\\)? choose 1 answer: a…
which of the following is equivalent to \\(\\frac{\\log(t)}{\\log_{8}(t)}\\)? choose 1 answer: a \\(\\log(8)\\) b \\(\\log_{8}(t^2)\\) c \\(\\frac{1}{\\log(8)}\\) d \\(\\frac{1}{\\log_{8}(t^2)}\\)
Answer
Explanation:
Step1: Apply change of base rule
Recall the change of base formula: $\log_b(a) = \frac{\log(a)}{\log(b)}$. Rearrange the given expression: $\frac{\log(t)}{\log_8(t)} = \frac{\log(t)}{\frac{\log(t)}{\log(8)}}$
Step2: Simplify the fraction
Cancel $\log(t)$ (where $\log(t) \neq 0$) and simplify: $\frac{\log(t)}{\frac{\log(t)}{\log(8)}} = \log(8)$
Answer:
A. $\log(8)$