What is (ln(77)-12ln(2))/(12ln(2)) ?

The solution to (ln(77)-12ln(2))/(12ln(2)) is (ln(77/4096))/(12ln(2))

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simplify (ln(77)-12ln(2))/(12ln(2))

simplify

\frac{ln ( 77 ) - 12 ln ( 2 )}{12 ln ( 2 )}

\frac{ln ( \frac{77}{4096} )}{12 ln ( 2 )}

Decimal Notation

- 0.47776 \dots

Solution steps

\frac{ln ( 77 ) - 12 ln ( 2 )}{12 ln ( 2 )}

Apply log rule:

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

12 ln (2) = ln (2^{12})

= \frac{ln ( 77 ) - ln ( 2 ^{12} )}{12 ln ( 2 )}

Apply log rule:

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

ln (77) - ln (2^{12}) = ln (\frac{77}{2 ^{12}})

= \frac{ln ( \frac{77}{2 ^{12}} )}{12 ln ( 2 )}

2^{12} = 4096

= \frac{ln ( \frac{77}{4096} )}{12 ln ( 2 )}

ln (\frac{1 \cdot 1 0 ^{- 4}}{1 \cdot 1 0 ^{- 3}})

lo g_{v} (b^{4}) (b^{9})

lo g_{6} ((\frac{u}{v ^{6}})^{5})

- ln (1 - x) + ln (1 - y)

ln (13) - ln (5)

What is (ln(77)-12ln(2))/(12ln(2)) ?
The solution to (ln(77)-12ln(2))/(12ln(2)) is (ln(77/4096))/(12ln(2))