Solve the Logarithmic Fraction: log₈5 ÷ log₈9

Question

$\frac{\log_85}{\log_89}=$

00:00 Solve

00:04 We'll use the formula for logical division

00:10 We'll get the log of the numerator in base of the denominator

00:20 We'll use this formula in our exercise

00:28 And this is the solution to the question

To solve this problem, let's simplify the given expression $\frac{\log_85}{\log_89}$ .

Step 1: Recognize that both the numerator and denominator have the same base, 8.
Step 2: The division property of logarithms states that $\frac{\log_b M}{\log_b N} = \log_N M$ .
Step 3: Apply the division rule to the given expression: $\frac{\log_8 5}{\log_8 9} = \log_9 5$ .

Thus, after simplifying, we see that $\frac{\log_85}{\log_89} = \log_9 5$ .

Hence, the correct answer is $\log_9 5$ , which corresponds to the choice 1.

$\log_95$