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

The solution to (-5ln(7)-ln(5))/(7ln(5)-ln(7)) is (-5ln(7)-ln(5))/(ln(78125/7))

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

simplify

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

\frac{- 5 ln ( 7 ) - ln ( 5 )}{ln ( \frac{78125}{7} )}

Decimal Notation

- 1.21660 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

5^{7} = 78125

= \frac{- 5 ln ( 7 ) - ln ( 5 )}{ln ( \frac{78125}{7} )}

ln (r e^{i θ})

lo g_{2} (x + 1) + 3 lo g_{2} (x) - 8 lo g_{4} (x)

\frac{1}{2} lo g_{10} (c) + 5 lo g_{10} (d)

lo g_{6} (x^{4} y^{6})

What is (-5ln(7)-ln(5))/(7ln(5)-ln(7)) ?
The solution to (-5ln(7)-ln(5))/(7ln(5)-ln(7)) is (-5ln(7)-ln(5))/(ln(78125/7))