What is ln|3-2|-3/2 ln|2*3-1|+2ln|3+3| ?

The solution to ln|3-2|-3/2 ln|2*3-1|+2ln|3+3| is ln((36sqrt(5))/(25))

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simplify ln|3-2|-3/2 ln|2*3-1|+2ln|3+3|

simplify

ln ∣ 3 - 2 ∣ - \frac{3}{2} ln ∣ 2 \cdot 3 - 1 ∣ + 2 ln ∣ 3 + 3 ∣

ln (\frac{36 5}{25})

Decimal Notation

1.16936 \dots

Solution steps

ln ∣ 3 - 2 ∣ - \frac{3}{2} ln ∣ 2 \cdot 3 - 1 ∣ + 2 ln ∣ 3 + 3 ∣

Apply log rule:

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

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

= ln ∣ 3 - 2 ∣ - ln (∣ 2 \cdot 3 - 1 ∣^{\frac{3}{2}}) + 2 ln ∣ 3 + 3 ∣

Apply log rule:

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

2 ln ∣ 3 + 3 ∣ = ln (∣ 3 + 3 ∣^{2})

= ln ∣ 3 - 2 ∣ - ln (∣ 2 \cdot 3 - 1 ∣^{\frac{3}{2}}) + ln (∣ 3 + 3 ∣^{2})

Apply log rule:

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

ln (∣ 3 + 3 ∣^{2}) - ln (∣ 2 \cdot 3 - 1 ∣^{\frac{3}{2}}) = ln (\frac{∣ 3 + 3 ∣ ^{2}}{∣ 2 \cdot 3 - 1 ∣ ^{\frac{3}{2}}})

= ln ∣ 3 - 2 ∣ + ln (\frac{∣ 3 + 3 ∣ ^{2}}{∣ 2 \cdot 3 - 1 ∣ ^{\frac{3}{2}}})

\frac{∣ 3 + 3 ∣ ^{2}}{∣ 2 \cdot 3 - 1 ∣ ^{\frac{3}{2}}} = \frac{36 5}{25}

= ln ∣ 3 - 2 ∣ + ln (\frac{36 5}{25})

ln ∣ 3 - 2 ∣ = 0

= 0 + ln (\frac{36 5}{25})

0 + ln (\frac{36 5}{25}) = ln (\frac{36 5}{25})

= ln (\frac{36 5}{25})

lo g_{2} (\frac{a ^{2} - 9}{8})

- lo g_{10} (6.5 \cdot 1 0^{- 3})

ln (\frac{9}{7 x ^{7} y})

ln (\frac{8}{2})

lo g_{10} (\frac{x y}{z})

What is ln|3-2|-3/2 ln|2*3-1|+2ln|3+3| ?
The solution to ln|3-2|-3/2 ln|2*3-1|+2ln|3+3| is ln((36sqrt(5))/(25))