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Question

If f(x)=logx(lnx), then

A
f(e)=e
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B
f(e)=1e
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C
f(e2)=1e2
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D
f(e2)=(1ln2)(2e)2
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Solution

The correct options are
B f(e)=1e
D f(e2)=(1ln2)(2e)2
Given function
f(x)=logx(lnx)=loge(logex)(logex)f(x)=logex×1x×1logex1x×loge(logex)(logex)2f(x)=1x[1loge(logex)](logex)2

So,
f(e)=1e and
f(e2)=1e2[1loge2]4f(e2)=(1loge2)(2e)2

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