What is ln(a)-ln(b)-ln(c) ?

The solution to ln(a)-ln(b)-ln(c) is ln(a/(bc))

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simplify ln(a)-ln(b)-ln(c)

simplify

ln (a) - ln (b) - ln (c)

ln (\frac{a}{b c})

Solution steps

ln (a) - ln (b) - ln (c)

Apply log rule:

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

ln (a) - ln (b) = ln (\frac{a}{b})

= ln (\frac{a}{b}) - ln (c)

Apply log rule:

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

ln (\frac{a}{b}) - ln (c) = ln (\frac{\frac{a}{b}}{c})

= ln (\frac{\frac{a}{b}}{c})

Apply the fraction rule:

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

= ln (\frac{a}{b c})

ln (\frac{6}{1})

lo g_{5} (4) + lo g_{5} (9)

\frac{1}{5800} ln (\frac{1}{2})

3 lo g_{10} (4) + 2 lo g_{10} (x)