What is (ln(21)-3ln(2))/(5ln(2)) ?

The solution to (ln(21)-3ln(2))/(5ln(2)) is (ln(21/8))/(5ln(2))

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simplify (ln(21)-3ln(2))/(5ln(2))

simplify

\frac{ln ( 21 ) - 3 ln ( 2 )}{5 ln ( 2 )}

\frac{ln ( \frac{21}{8} )}{5 ln ( 2 )}

Decimal Notation

0.27846 \dots

Solution steps

\frac{ln ( 21 ) - 3 ln ( 2 )}{5 ln ( 2 )}

Apply log rule:

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

3 ln (2) = ln (2^{3})

= \frac{ln ( 21 ) - ln ( 2 ^{3} )}{5 ln ( 2 )}

Apply log rule:

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

ln (21) - ln (2^{3}) = ln (\frac{21}{2 ^{3}})

= \frac{ln ( \frac{21}{2 ^{3}} )}{5 ln ( 2 )}

2^{3} = 8

= \frac{ln ( \frac{21}{8} )}{5 ln ( 2 )}

ln (\frac{4}{15})

lo g_{10} (\frac{x}{1000 y ^{2}})

ln (\frac{e}{x y ^{2}})

ln (\frac{37}{38})

ln (2 x) + 2 ln (y) - 5 ln (z)

What is (ln(21)-3ln(2))/(5ln(2)) ?
The solution to (ln(21)-3ln(2))/(5ln(2)) is (ln(21/8))/(5ln(2))