What is ln(3)-ln(6)-ln(5) ?

The solution to ln(3)-ln(6)-ln(5) is -ln(10)

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simplify ln(3)-ln(6)-ln(5)

simplify

ln (3) - ln (6) - ln (5)

- ln (10)

Decimal Notation

- 2.30258 \dots

Solution steps

ln (3) - ln (6) - ln (5)

Apply log rule:

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

ln (3) - ln (6) = ln (\frac{3}{6})

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

Cancel the common factor:

3

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

Apply log rule:

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

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

= ln (\frac{\frac{1}{2}}{5})

\frac{\frac{1}{2}}{5} = \frac{1}{10}

= ln (\frac{1}{10})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (10)

y - ln (y + 1) - ln (x) + x

ln (y^{2} + 4) - ln (y^{2} - 2)

ln (x^{- 1}) - ln (3)

ln (\frac{0.692}{0.0112})

ln (\frac{505}{760})