What is simplify-2ln(3/4)-ln(6) ?

The solution to simplify-2ln(3/4)-ln(6) is -ln(27/8)

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simplify-2ln(3/4)-ln(6)

simplify

- 2 ln (\frac{3}{4}) - ln (6)

- ln (\frac{27}{8})

Decimal

- 1.21639 \dots

Solution steps

- 2 ln (\frac{3}{4}) - ln (6)

Apply log rule:

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

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

= - ln ((\frac{3}{4})^{2}) - ln (6)

Rewrite

- ln ((\frac{3}{4})^{2}) - ln (6)

- (ln ((\frac{3}{4})^{2}) + ln (6))

= - (ln (6) + ln ((\frac{3}{4})^{2}))

Apply log rule:

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

ln ((\frac{3}{4})^{2}) + ln (6) = ln (6 (\frac{3}{4})^{2})

= - ln (6 (\frac{3}{4})^{2})

(\frac{3}{4})^{2} \cdot 6 = \frac{27}{8}

= - ln (\frac{27}{8})

3 (lo g_{6} (x) + 2 lo g_{6} (y) - 3 lo g_{6} (z))

ln (\frac{2 x - 2}{9 - x ^{2}})

ln (\frac{7}{e})

0.04 + 0.36 lo g_{10} (2) + 0.57 lo g_{10} (5)

ln (\frac{x ^{3} y}{z})

What is simplify-2ln(3/4)-ln(6) ?
The solution to simplify-2ln(3/4)-ln(6) is -ln(27/8)