What is (2ln(3)-ln(4))-(2ln(1)-ln(2)) ?

The solution to (2ln(3)-ln(4))-(2ln(1)-ln(2)) is ln(9/4)+ln(2)

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simplify (2ln(3)-ln(4))-(2ln(1)-ln(2))

simplify

(2 ln (3) - ln (4)) - (2 ln (1) - ln (2))

ln (\frac{9}{4}) + ln (2)

Decimal Notation

1.50407 \dots

Solution steps

(2 ln (3) - ln (4)) - (2 ln (1) - ln (2))

Apply log rule:

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

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

= (ln (3^{2}) - ln (4)) - (2 ln (1) - ln (2))

Apply log rule:

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

ln (3^{2}) - ln (4) = ln (\frac{3 ^{2}}{4})

= ln (\frac{3 ^{2}}{4}) - (2 ln (1) - ln (2))

3^{2} = 9

= ln (\frac{9}{4}) - (2 ln (1) - ln (2))

- (2 ln (1) - ln (2)) = ln (2)

= ln (\frac{9}{4}) + ln (2)

10 \cdot lo g_{10} (\frac{5 \cdot 1 0 ^{- 6}}{1 \cdot 1 0 ^{- 12}})

100 + 20 \cdot ln (\frac{65}{65 - 23})

ln (\frac{4}{9}) \cdot \frac{20}{ln ( \frac{4}{11} )}

ln ((- 2.772)^{19.764})

\frac{1}{2} ln ∣ 2 (12) + 1 ∣ + 2 ln ∣ 12 - 1 ∣

What is (2ln(3)-ln(4))-(2ln(1)-ln(2)) ?
The solution to (2ln(3)-ln(4))-(2ln(1)-ln(2)) is ln(9/4)+ln(2)