What is (-31ln(3)-14ln(2))/(2ln(2)-ln(3)) ?

The solution to (-31ln(3)-14ln(2))/(2ln(2)-ln(3)) is (-31ln(3)-14ln(2))/(ln(4/3))

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simplify (-31ln(3)-14ln(2))/(2ln(2)-ln(3))

simplify

\frac{- 31 ln ( 3 ) - 14 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

\frac{- 31 ln ( 3 ) - 14 ln ( 2 )}{ln ( \frac{4}{3} )}

Decimal Notation

- 152.11598 \dots

Solution steps

\frac{- 31 ln ( 3 ) - 14 ln ( 2 )}{2 ln ( 2 ) - ln ( 3 )}

Apply log rule:

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

2 ln (2) = ln (2^{2})

= \frac{- 31 ln ( 3 ) - 14 ln ( 2 )}{ln ( 2 ^{2} ) - ln ( 3 )}

Apply log rule:

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

ln (2^{2}) - ln (3) = ln (\frac{2 ^{2}}{3})

= \frac{- 31 ln ( 3 ) - 14 ln ( 2 )}{ln ( \frac{2 ^{2}}{3} )}

2^{2} = 4

= \frac{- 31 ln ( 3 ) - 14 ln ( 2 )}{ln ( \frac{4}{3} )}

ln (x - 2) - ln (x + 2)

lo g_{6} (\frac{x}{x ^{5}})

- lo g_{10} (3.3 \cdot 1 0^{- 10})

lo g_{10} (\frac{19}{z})

lo g_{10} (6 x^{11})

What is (-31ln(3)-14ln(2))/(2ln(2)-ln(3)) ?
The solution to (-31ln(3)-14ln(2))/(2ln(2)-ln(3)) is (-31ln(3)-14ln(2))/(ln(4/3))