What is (6ln(7)-2ln(5))/(-ln(5)-5ln(7)) ?

The solution to (6ln(7)-2ln(5))/(-ln(5)-5ln(7)) is (ln(117649/25))/(-ln(5)-5ln(7))

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simplify (6ln(7)-2ln(5))/(-ln(5)-5ln(7))

simplify

\frac{6 ln ( 7 ) - 2 ln ( 5 )}{- ln ( 5 ) - 5 ln ( 7 )}

\frac{ln ( \frac{117649}{25} )}{- ln ( 5 ) - 5 ln ( 7 )}

Decimal Notation

- 0.74579 \dots

Solution steps

\frac{6 ln ( 7 ) - 2 ln ( 5 )}{- ln ( 5 ) - 5 ln ( 7 )}

Apply log rule:

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

6 ln (7) = ln (7^{6})

= \frac{ln ( 7 ^{6} ) - 2 ln ( 5 )}{- ln ( 5 ) - 5 ln ( 7 )}

Apply log rule:

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

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

= \frac{ln ( 7 ^{6} ) - ln ( 5 ^{2} )}{- ln ( 5 ) - 5 ln ( 7 )}

Apply log rule:

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

ln (7^{6}) - ln (5^{2}) = ln (\frac{7 ^{6}}{5 ^{2}})

= \frac{ln ( \frac{7 ^{6}}{5 ^{2}} )}{- ln ( 5 ) - 5 ln ( 7 )}

\frac{7 ^{6}}{5 ^{2}} = \frac{117649}{25}

= \frac{ln ( \frac{117649}{25} )}{- ln ( 5 ) - 5 ln ( 7 )}

20 \cdot lo g_{10} (\frac{4 π \cdot 2}{644334})

\frac{4}{3} lo g_{3} (2)

lo g_{2} (\frac{6 ^{4}}{1 1 ^{6}})

ln (20) - ln (3)

ln (x - 1) - ln (3 x + 2)

What is (6ln(7)-2ln(5))/(-ln(5)-5ln(7)) ?
The solution to (6ln(7)-2ln(5))/(-ln(5)-5ln(7)) is (ln(117649/25))/(-ln(5)-5ln(7))