What is (3ln(5)-3ln(7))/(2ln(7)-ln(5)) ?

The solution to (3ln(5)-3ln(7))/(2ln(7)-ln(5)) is (ln(125/343))/(ln(49/5))

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simplify (3ln(5)-3ln(7))/(2ln(7)-ln(5))

simplify

\frac{3 ln ( 5 ) - 3 ln ( 7 )}{2 ln ( 7 ) - ln ( 5 )}

\frac{ln ( \frac{125}{343} )}{ln ( \frac{49}{5} )}

Decimal Notation

- 0.44226 \dots

Solution steps

\frac{3 ln ( 5 ) - 3 ln ( 7 )}{2 ln ( 7 ) - ln ( 5 )}

Apply log rule:

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

3 ln (5) = ln (5^{3})

= \frac{ln ( 5 ^{3} ) - 3 ln ( 7 )}{2 ln ( 7 ) - ln ( 5 )}

Apply log rule:

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

3 ln (7) = ln (7^{3})

= \frac{ln ( 5 ^{3} ) - ln ( 7 ^{3} )}{2 ln ( 7 ) - ln ( 5 )}

Apply log rule:

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

ln (5^{3}) - ln (7^{3}) = ln (\frac{5 ^{3}}{7 ^{3}})

= \frac{ln ( \frac{5 ^{3}}{7 ^{3}} )}{2 ln ( 7 ) - ln ( 5 )}

\frac{5 ^{3}}{7 ^{3}} = \frac{125}{343}

= \frac{ln ( \frac{125}{343} )}{2 ln ( 7 ) - ln ( 5 )}

Apply log rule:

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

2 ln (7) = ln (7^{2})

= \frac{ln ( \frac{125}{343} )}{ln ( 7 ^{2} ) - ln ( 5 )}

Apply log rule:

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

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

= \frac{ln ( \frac{125}{343} )}{ln ( \frac{7 ^{2}}{5} )}

7^{2} = 49

= \frac{ln ( \frac{125}{343} )}{ln ( \frac{49}{5} )}

ln (\frac{2 i + 1}{- 1})

\frac{5 ln ( 3 )}{ln ( \frac{2}{3} )}

(2 \cdot 8.314) \cdot ln (\frac{1.5}{7})

- 5 ln (60 + \frac{5}{3} - 39) + 74.05 + 5 ln (\frac{5}{3})

- lo g_{10} (8.1 \cdot 1 0^{- 3})

What is (3ln(5)-3ln(7))/(2ln(7)-ln(5)) ?
The solution to (3ln(5)-3ln(7))/(2ln(7)-ln(5)) is (ln(125/343))/(ln(49/5))