What is (-4ln(2)-7ln(7))/(5ln(7)-ln(2)) ?

The solution to (-4ln(2)-7ln(7))/(5ln(7)-ln(2)) is (-4ln(2)-7ln(7))/(ln(16807/2))

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simplify (-4ln(2)-7ln(7))/(5ln(7)-ln(2))

simplify

\frac{- 4 ln ( 2 ) - 7 ln ( 7 )}{5 ln ( 7 ) - ln ( 2 )}

\frac{- 4 ln ( 2 ) - 7 ln ( 7 )}{ln ( \frac{16807}{2} )}

Decimal Notation

- 1.81421 \dots

Solution steps

\frac{- 4 ln ( 2 ) - 7 ln ( 7 )}{5 ln ( 7 ) - ln ( 2 )}

Apply log rule:

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

5 ln (7) = ln (7^{5})

= \frac{- 4 ln ( 2 ) - 7 ln ( 7 )}{ln ( 7 ^{5} ) - ln ( 2 )}

Apply log rule:

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

ln (7^{5}) - ln (2) = ln (\frac{7 ^{5}}{2})

= \frac{- 4 ln ( 2 ) - 7 ln ( 7 )}{ln ( \frac{7 ^{5}}{2} )}

7^{5} = 16807

= \frac{- 4 ln ( 2 ) - 7 ln ( 7 )}{ln ( \frac{16807}{2} )}

ln (\frac{A}{B})

lo g_{9} (x) + lo g_{9} (x + 8)

lo g_{10} (x^{9} z)

- lo g_{10} (6.4 \times 1 0^{- 5})

lo g_{4} ((\frac{1024}{x y ^{2}})^{2})

What is (-4ln(2)-7ln(7))/(5ln(7)-ln(2)) ?
The solution to (-4ln(2)-7ln(7))/(5ln(7)-ln(2)) is (-4ln(2)-7ln(7))/(ln(16807/2))