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

The solution to ln(y)-ln(c)-ln(x) is ln(y/(cx))

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simplify ln(y)-ln(c)-ln(x)

simplify

ln (y) - ln (c) - ln (x)

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

Solution steps

ln (y) - ln (c) - ln (x)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

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

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

ln (1 + x^{2}) - ln (x)

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ln (\frac{2}{1 - 0 - ( - 1 )})

ln (8) + ln (x) - ln (y)

- lo g_{2} (10 x)