What is (-6ln(8))/(ln(8)-ln(5)) ?

The solution to (-6ln(8))/(ln(8)-ln(5)) is -(18ln(2))/(ln(8/5))

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simplify (-6ln(8))/(ln(8)-ln(5))

simplify

\frac{- 6 ln ( 8 )}{ln ( 8 ) - ln ( 5 )}

- \frac{18 ln ( 2 )}{ln ( \frac{8}{5} )}

Decimal Notation

- 26.54585 \dots

Solution steps

\frac{- 6 ln ( 8 )}{ln ( 8 ) - ln ( 5 )}

Apply log rule:

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

ln (8) - ln (5) = ln (\frac{8}{5})

= \frac{- 6 ln ( 8 )}{ln ( \frac{8}{5} )}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{6 ln ( 8 )}{ln ( \frac{8}{5} )}

Simplify

ln (8) : 3 ln (2)

= - \frac{6 \cdot 3 ln ( 2 )}{ln ( \frac{8}{5} )}

Multiply the numbers:

6 \cdot 3 = 18

= - \frac{18 ln ( 2 )}{ln ( \frac{8}{5} )}

ln (2) - ln (- 2)

ln (\frac{131}{2})

lo g_{10} (\frac{x}{y ^{2} z})

2 lo g_{2} (3) - 5 lo g_{2} (x) + 2 lo g_{2} (4)

ln (c) - ln (d) + ln (0.017 + c) - ln (0.017 - d)

What is (-6ln(8))/(ln(8)-ln(5)) ?
The solution to (-6ln(8))/(ln(8)-ln(5)) is -(18ln(2))/(ln(8/5))