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

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

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

simplify

2 ln (3) - ln (4) + ln (2)

ln (\frac{9}{2})

Decimal Notation

1.50407 \dots

Solution steps

2 ln (3) - ln (4) + 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) + 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}) + ln (2)

3^{2} = 9

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

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

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

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

\frac{9}{4} \cdot 2 = \frac{9}{2}

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

ln (\frac{( 0.667 - 1 )}{( \frac{2}{3} \cdot 0.8749 - 1 )})

\frac{π}{8} ln (6)

- ln (2) + 2 ln (3) + 4 ln (5)

\frac{1}{7} ln ∣ 9.3 + 1 ∣ - \frac{1}{7} ln ∣ 9.3 + 8 ∣ + C