What is join-(6ln(5/8))/(ln(2)) ?

The solution to join-(6ln(5/8))/(ln(2)) is -(ln(15625/262144))/(ln(2))

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join-(6ln(5/8))/(ln(2))

join

- \frac{6 ln ( \frac{5}{8} )}{ln ( 2 )}

- \frac{ln ( \frac{15625}{262144} )}{ln ( 2 )}

Decimal Notation

4.06843 \dots

Solution steps

- \frac{6 ln ( \frac{5}{8} )}{ln ( 2 )}

Apply log rule:

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

6 ln (\frac{5}{8}) = ln ((\frac{5}{8})^{6})

= - \frac{ln ( ( \frac{5}{8} ) ^{6} )}{ln ( 2 )}

(\frac{5}{8})^{6} = \frac{5 ^{6}}{8 ^{6}}

= - \frac{ln ( \frac{5 ^{6}}{8 ^{6}} )}{ln ( 2 )}

\frac{5 ^{6}}{8 ^{6}} = \frac{15625}{262144}

= - \frac{ln ( \frac{15625}{262144} )}{ln ( 2 )}

ln (e^{y} (y - 1))

- lo g_{10} (3.2 \cdot 1 0^{- 3})

182000 \cdot [ln (0.63) - ln (1.3)]

ln (\frac{2 x}{2 + x})

lo g_{8} (3^{7}) + lo g_{8} (5^{7}) - lo g_{8} (1 6^{7})

What is join-(6ln(5/8))/(ln(2)) ?
The solution to join-(6ln(5/8))/(ln(2)) is -(ln(15625/262144))/(ln(2))