What is 7/2 ln(ln(e^x))-ln(sqrt(e^{6ln(x))}) ?

The solution to 7/2 ln(ln(e^x))-ln(sqrt(e^{6ln(x))}) is ln(x^{1/2})

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simplify 7/2 ln(ln(e^x))-ln(sqrt(e^{6ln(x))})

simplify

\frac{7}{2} ln (ln (e^{x})) - ln (e^{6 l n (x)})

ln (x^{\frac{1}{2}})

Solution steps

\frac{7}{2} ln (ln (e^{x})) - ln (e^{6 l n (x)})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{7}{2} ln (ln (e^{x})) = ln (ln^{\frac{7}{2}} (e^{x}))

= ln (ln^{\frac{7}{2}} (e^{x})) - ln (e^{6 l n (x)})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (ln^{\frac{7}{2}} (e^{x})) - ln (e^{6 l n (x)}) = ln (\frac{ln ^{\frac{7}{2}} ( e ^{x} )}{e ^{6 l n (x)}})

= ln (\frac{ln ^{\frac{7}{2}} ( e ^{x} )}{e ^{6 l n (x)}})

Simplify

\frac{ln ^{\frac{7}{2}} ( e ^{x} )}{e ^{6 l n (x)}} : x^{\frac{1}{2}}

= ln (x^{\frac{1}{2}})

lo g_{5} (\frac{a ^{3}}{b ^{3}})

lo g_{7} ((m + n) \cdot p)

lo g_{10} (\frac{x}{10000 y ^{9}})

lo g_{10} (\frac{x ^{6} y}{z})

lo g_{2} (3) + lo g_{2} (x)

What is 7/2 ln(ln(e^x))-ln(sqrt(e^{6ln(x))}) ?
The solution to 7/2 ln(ln(e^x))-ln(sqrt(e^{6ln(x))}) is ln(x^{1/2})