What is (3ln(20))/(2ln(19)-ln(20)) ?

The solution to (3ln(20))/(2ln(19)-ln(20)) is (3ln(20))/(ln(361/20))

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simplify (3ln(20))/(2ln(19)-ln(20))

simplify

\frac{3 ln ( 20 )}{2 ln ( 19 ) - ln ( 20 )}

\frac{3 ln ( 20 )}{ln ( \frac{361}{20} )}

Decimal Notation

3.10637 \dots

Solution steps

\frac{3 ln ( 20 )}{2 ln ( 19 ) - ln ( 20 )}

Apply log rule:

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

2 ln (19) = ln (1 9^{2})

= \frac{3 ln ( 20 )}{ln ( 1 9 ^{2} ) - ln ( 20 )}

Apply log rule:

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

ln (1 9^{2}) - ln (20) = ln (\frac{1 9 ^{2}}{20})

= \frac{3 ln ( 20 )}{ln ( \frac{1 9 ^{2}}{20} )}

1 9^{2} = 361

= \frac{3 ln ( 20 )}{ln ( \frac{361}{20} )}

- \frac{5}{14} \cdot lo g_{2} (\frac{5}{14}) - \frac{9}{14} \cdot lo g_{2} (\frac{9}{14})

lo g_{10} ((1 + i)^{- 20})

ln (\frac{55}{50}) + ((0.06 + 0.4) \cdot 0.5)

lo g_{10} (\frac{7 y ^{3}}{4 x ^{2}})

(- 0.94 + 1.96 \cdot 0.21) \cdot (ln (7.9) - ln (7.5) \cdot 100)

What is (3ln(20))/(2ln(19)-ln(20)) ?
The solution to (3ln(20))/(2ln(19)-ln(20)) is (3ln(20))/(ln(361/20))