What is (15ln(7)-6ln(2))/(2ln(28)) ?

The solution to (15ln(7)-6ln(2))/(2ln(28)) is (ln(\frac{7^{15})/(64))}{2ln(28)}

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simplify (15ln(7)-6ln(2))/(2ln(28))

simplify

\frac{15 ln ( 7 ) - 6 ln ( 2 )}{2 ln ( 28 )}

\frac{ln ( \frac{7 ^{15}}{64} )}{2 ln ( 28 )}

Decimal Notation

3.75573 \dots

Solution steps

\frac{15 ln ( 7 ) - 6 ln ( 2 )}{2 ln ( 28 )}

Apply log rule:

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

15 ln (7) = ln (7^{15})

= \frac{ln ( 7 ^{15} ) - 6 ln ( 2 )}{2 ln ( 28 )}

Apply log rule:

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

6 ln (2) = ln (2^{6})

= \frac{ln ( 7 ^{15} ) - ln ( 2 ^{6} )}{2 ln ( 28 )}

Apply log rule:

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

ln (7^{15}) - ln (2^{6}) = ln (\frac{7 ^{15}}{2 ^{6}})

= \frac{ln ( \frac{7 ^{15}}{2 ^{6}} )}{2 ln ( 28 )}

2^{6} = 64

= \frac{ln ( \frac{7 ^{15}}{64} )}{2 ln ( 28 )}

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What is (15ln(7)-6ln(2))/(2ln(28)) ?
The solution to (15ln(7)-6ln(2))/(2ln(28)) is (ln(\frac{7^{15})/(64))}{2ln(28)}