What is (ln(3025/81)-16ln(2))/(ln(2)) ?

The solution to (ln(3025/81)-16ln(2))/(ln(2)) is (ln(3025/5308416))/(ln(2))

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simplify (ln(3025/81)-16ln(2))/(ln(2))

simplify

\frac{ln ( \frac{3025}{81} ) - 16 ln ( 2 )}{ln ( 2 )}

\frac{ln ( \frac{3025}{5308416} )}{ln ( 2 )}

Decimal Notation

- 10.77713 \dots

Solution steps

\frac{ln ( \frac{3025}{81} ) - 16 ln ( 2 )}{ln ( 2 )}

Apply log rule:

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

16 ln (2) = ln (2^{16})

= \frac{ln ( \frac{3025}{81} ) - ln ( 2 ^{16} )}{ln ( 2 )}

Apply log rule:

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

ln (\frac{3025}{81}) - ln (2^{16}) = ln (\frac{\frac{3025}{81}}{2 ^{16}})

= \frac{ln ( \frac{\frac{3025}{81}}{2 ^{16}} )}{ln ( 2 )}

\frac{\frac{3025}{81}}{2 ^{16}} = \frac{3025}{5308416}

= \frac{ln ( \frac{3025}{5308416} )}{ln ( 2 )}

ln (\frac{28.3}{23.1})

ln (x) - 3 ln (y) + \frac{1}{2} ln (z)

ln (\frac{1}{6.5})

ln (\frac{0.02}{0.01})

What is (ln(3025/81)-16ln(2))/(ln(2)) ?
The solution to (ln(3025/81)-16ln(2))/(ln(2)) is (ln(3025/5308416))/(ln(2))