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Popular >

simplify ln(y/x-1)-ln(x)

Solution

simplify

ln (\frac{y}{x} - 1) - ln (x)

Solution

ln (\frac{y - x}{x ^{2}})

Solution steps

ln (\frac{y}{x} - 1) - ln (x)

Apply log rule:

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

ln (\frac{y}{x} - 1) - ln (x) = ln (\frac{\frac{y}{x} - 1}{x})

= ln (\frac{\frac{y}{x} - 1}{x})

Simplify

\frac{\frac{y}{x} - 1}{x} : \frac{y - x}{x ^{2}}

= ln (\frac{y - x}{x ^{2}})

Popular Examples

simplify-log_{10}(5.1*10^{-11})simplify

- lo g_{10} (5.1 \cdot 1 0^{- 11})

simplify 2ln(4/3)simplify

2 ln (\frac{4}{3})

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ln (\frac{2}{x ^{2}})

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(\frac{1}{2 x})^{2} + ln (\frac{1}{2 x})

Frequently Asked Questions (FAQ)

What is ln(y/x-1)-ln(x) ?
The solution to ln(y/x-1)-ln(x) is ln((y-x)/(x^2))