What is ((6ln(x)+16-6ln(4)))/x ?

The solution to ((6ln(x)+16-6ln(4)))/x is (ln((x^6)/(4096))+16)/x

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simplify ((6ln(x)+16-6ln(4)))/x

simplify

\frac{( 6 ln ( x ) + 16 - 6 ln ( 4 ) )}{x}

\frac{ln ( \frac{x ^{6}}{4096} ) + 16}{x}

Solution steps

\frac{( 6 ln ( x ) + 16 - 6 ln ( 4 ) )}{x}

Apply log rule:

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

6 ln (x) = ln (x^{6})

= \frac{( ln ( x ^{6} ) + 16 - 6 ln ( 4 ) )}{x}

Apply log rule:

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

6 ln (4) = ln (4^{6})

= \frac{( ln ( x ^{6} ) + 16 - ln ( 4 ^{6} ) )}{x}

Apply log rule:

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

ln (x^{6}) - ln (4^{6}) = ln (\frac{x ^{6}}{4 ^{6}})

= \frac{ln ( \frac{x ^{6}}{4 ^{6}} ) + 16}{x}

4^{6} = 4096

= \frac{ln ( \frac{x ^{6}}{4096} ) + 16}{x}

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What is ((6ln(x)+16-6ln(4)))/x ?
The solution to ((6ln(x)+16-6ln(4)))/x is (ln((x^6)/(4096))+16)/x