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

The solution to (-5ln(5)-4ln(2))/(7ln(5)-ln(2)) is (-5ln(5)-4ln(2))/(ln(78125/2))

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

simplify

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

\frac{- 5 ln ( 5 ) - 4 ln ( 2 )}{ln ( \frac{78125}{2} )}

Decimal Notation

- 1.02334 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

5^{7} = 78125

= \frac{- 5 ln ( 5 ) - 4 ln ( 2 )}{ln ( \frac{78125}{2} )}

38 \cdot ln (\frac{400}{600}) - 8.314 \cdot ln (\frac{1}{10})

ln (\frac{1}{5}) - e^{(- 5^{3})}

8 \cdot ln (\frac{8}{9.1161})

lo g_{10} (\frac{1}{2.5 \cdot 1 0 ^{- 9}})

- 2 ln (\frac{3 e ^{- n^{3} + n x}}{x})

What is (-5ln(5)-4ln(2))/(7ln(5)-ln(2)) ?
The solution to (-5ln(5)-4ln(2))/(7ln(5)-ln(2)) is (-5ln(5)-4ln(2))/(ln(78125/2))