What is the value of log, base, 4, start fraction, 1, divided by, 16, end fractionlog 4 161 ?
Question
What is the value of log, base, 4, start fraction, 1, divided by, 16, end fraction log 4 161 ?
Solution
The value of log base 4 of 1/16 can be found by using the property of logarithms that says log_b(a^n) = n * log_b(a).
Step 1: Recognize that 16 is 4^2. So, 1/16 is the same as 4^-2.
Step 2: Substitute 4^-2 into the logarithm: log_4(4^-2).
Step 3: Use the property of logarithms to simplify: -2 * log_4(4).
Step 4: The log base 4 of 4 is 1, so the expression simplifies to -2 * 1.
Step 5: Therefore, log base 4 of 1/16 is -2.
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