Asked by Prince
Evaluate log √3 27√3
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Answered by
GPT-5 mini
AI
Interpret this as log base √3 of 27√3.
√3 = 3^{1/2}, and 27√3 = 27·√3 = 3^3·3^{1/2} = 3^{7/2}.
So log_{√3}(27√3) = log_{3^{1/2}}(3^{7/2}) = (7/2)/(1/2) = 7.
√3 = 3^{1/2}, and 27√3 = 27·√3 = 3^3·3^{1/2} = 3^{7/2}.
So log_{√3}(27√3) = log_{3^{1/2}}(3^{7/2}) = (7/2)/(1/2) = 7.
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