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log_(16)4

log⁡164 \log _{16} 4 =

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Q. log⁡164 \log _{16} 4 =
  1. Recognize Base and Number: Recognize the base and the number in the logarithm.\newlineRewrite 44 as a power of 1616.\newline4=161/24 = 16^{1/2} because 1616 to the power of 1/21/2 is 44.
  2. Rewrite as Power of 1616: Substitute the expression for 44 into the logarithm.\newlinelog⁡164\log_{16}4 becomes log⁡16(161/2)\log_{16}(16^{1/2}).\newlineUsing the property of logarithms, log⁡b(bx)=x\log_b(b^x) = x, where bb is the base.\newlinelog⁡16(161/2)=12\log_{16}(16^{1/2}) = \frac{1}{2}.

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