If f(x) = e^x and g(x) = log x show that fog=gof given x>0

Daniaal Sanchez

Daniaal Sanchez

Answered question


If f(x)=ex and g(x)=logx show that fog=gof given x>0

Answer & Explanation

Liyana Mansell

Liyana Mansell

Skilled2021-01-14Added 97 answers

E is a special number where ex differentiates to ex. ln(x) is log base e of x.
Given that log base 10 of 10 is 1, and log base n of n is 1, ln(e) is also 1.

So fg(x)=eg(x)=elogx=x. GF(x)=ln(f(x))=ln(ex)=xln(e) (using log laws, bringing power to the front), =x×1=x.
Therefore fg(x)=x=gf(x)

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