What is 2ln(3)-ln(x-1)+3ln(x) ?

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

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simplify 2ln(3)-ln(x-1)+3ln(x)

simplify

2 ln (3) - ln (x - 1) + 3 ln (x)

ln (\frac{9 x ^{3}}{x - 1})

Solution steps

2 ln (3) - ln (x - 1) + 3 ln (x)

Apply log rule:

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

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

= ln (3^{2}) - ln (x - 1) + 3 ln (x)

Apply log rule:

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

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

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

3^{2} = 9

= ln (\frac{9}{x - 1}) + 3 ln (x)

Apply log rule:

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

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

= ln (\frac{9}{x - 1}) + ln (x^{3})

Apply log rule:

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

ln (\frac{9}{x - 1}) + ln (x^{3}) = ln (\frac{9}{x - 1} x^{3})

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

lo g_{4} (\frac{16}{x})

- lo g_{10} (3.2 \cdot 1 0^{- 5})

lo g_{10} (\frac{p ^{2} q ^{3}}{r})

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