What is ln(z)-ln(x)-ln(y) ?

The solution to ln(z)-ln(x)-ln(y) is ln(z/(xy))

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simplify ln(z)-ln(x)-ln(y)

simplify

ln (z) - ln (x) - ln (y)

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

Solution steps

ln (z) - ln (x) - ln (y)

Apply log rule:

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

ln (z) - ln (x) = ln (\frac{z}{x})

= ln (\frac{z}{x}) - ln (y)

Apply log rule:

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

ln (\frac{z}{x}) - ln (y) = ln (\frac{\frac{z}{x}}{y})

= ln (\frac{\frac{z}{x}}{y})

Apply the fraction rule:

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

= ln (\frac{z}{x y})

6 lo g_{10} (q) + lo g_{10} (x)

ln (\frac{0.8}{2})

lo g_{b} (5 x y)

\frac{1}{2} lo g_{10} (a) + 5 lo g_{10} (b)

lo g_{10} (7 x^{3} y)