What is 2ln(6)-3ln(8) ?

The solution to 2ln(6)-3ln(8) is ln(9/128)

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simplify 2ln(6)-3ln(8)

simplify

2 ln (6) - 3 ln (8)

ln (\frac{9}{128})

Decimal Notation

- 2.65480 \dots

Solution steps

2 ln (6) - 3 ln (8)

Apply log rule:

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

2 ln (6) = ln (6^{2})

= ln (6^{2}) - 3 ln (8)

Apply log rule:

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

3 ln (8) = ln (8^{3})

= ln (6^{2}) - ln (8^{3})

Apply log rule:

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

ln (6^{2}) - ln (8^{3}) = ln (\frac{6 ^{2}}{8 ^{3}})

= ln (\frac{6 ^{2}}{8 ^{3}})

\frac{6 ^{2}}{8 ^{3}} = \frac{9}{128}

= ln (\frac{9}{128})

lo g_{10} (\frac{5 x y ^{2}}{z ^{3}})

ln (\frac{6.1 \cdot 7.36}{9.42 \cdot 1 0 ^{- 3}})

4 lo g_{10} (x) + 2 lo g_{10} (x - 1)

\frac{5 ln ( - 1 )}{6} - 3 \frac{1}{3}

\frac{1}{5} (6 ln (5) - ln (2))