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

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

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

simplify

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

ln (\frac{x}{yz})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

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

= ln (\frac{x}{yz})

lo g_{9} (2 x + 3) - lo g_{9} (\frac{1}{2 x - 3})

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

lo g_{10} (x^{2} - 16) - 2 lo g_{10} (x + 4)

2 lo g_{10} (x) + 3 lo g_{10} (x + 1)