What is (-ln(2)-5ln(x)-5)/x ?

The solution to (-ln(2)-5ln(x)-5)/x is (-ln(2x^5)-5)/x

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simplify (-ln(2)-5ln(x)-5)/x

simplify

\frac{- ln ( 2 ) - 5 ln ( x ) - 5}{x}

\frac{- ln ( 2 x ^{5} ) - 5}{x}

Solution steps

\frac{- ln ( 2 ) - 5 ln ( x ) - 5}{x}

Apply log rule:

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

5 ln (x) = ln (x^{5})

= \frac{- ln ( 2 ) - ln ( x ^{5} ) - 5}{x}

Rewrite

- ln (2) - ln (x^{5})

- (ln (2) + ln (x^{5}))

= \frac{- ( ln ( x ^{5} ) + ln ( 2 ) ) - 5}{x}

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (2) + ln (x^{5}) = ln (2 x^{5})

= \frac{- ln ( 2 x ^{5} ) - 5}{x}

\frac{1}{4} ln (\frac{7}{2})

2 lo g_{10} (x) + lo g_{10} (5 x - 8)

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

lo g_{e} (\frac{1}{4}) - lo g_{e} (4)

lo g_{4} \frac{( x ^{2} \cdot \frac{1 ^{2}}{3 ^{2}} y ^{2} )}{x}

What is (-ln(2)-5ln(x)-5)/x ?
The solution to (-ln(2)-5ln(x)-5)/x is (-ln(2x^5)-5)/x