Solve the Logarithmic Fraction: log₈5 ÷ log₈9

log⁡85log⁡89= \frac{\log_85}{\log_89}=

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Step-by-step video solution

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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

Step-by-step written solution

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1

Understand the problem

log⁡85log⁡89= \frac{\log_85}{\log_89}=

2

Step-by-step solution

To solve this problem, let's simplify the given expression log⁡85log⁡89\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 log⁡bMlog⁡bN=log⁡NM\frac{\log_b M}{\log_b N} = \log_N M.
  • Step 3: Apply the division rule to the given expression: log⁡85log⁡89=log⁡95\frac{\log_8 5}{\log_8 9} = \log_9 5.

Thus, after simplifying, we see that log⁡85log⁡89=log⁡95\frac{\log_85}{\log_89} = \log_9 5.

Hence, the correct answer is log⁡95\log_9 5, which corresponds to the choice 1.

3

Final Answer

log⁡95 \log_95

Practice Quiz

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\( \frac{1}{\log_49}= \)

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