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Popular >

simplify ln(x/y)-ln(a/b)

Solution

simplify

ln (\frac{x}{y}) - ln (\frac{a}{b})

Solution

ln (\frac{b x}{a y})

Solution steps

ln (\frac{x}{y}) - ln (\frac{a}{b})

Apply log rule:

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

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

= ln (\frac{\frac{x}{y}}{\frac{a}{b}})

Divide fractions:

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

= ln (\frac{b x}{a y})

Popular Examples

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- \frac{1}{2} ln (5 - 2 x) - ln (x)

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ln ∣ x ∣ + 2 ln (x^{2} + 4) + C

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ln (\frac{10}{22.5})

simplify 1/5 ln((170-75)/(115))simplify

\frac{1}{5} ln (\frac{170 - 75}{115})

Frequently Asked Questions (FAQ)

What is ln(x/y)-ln(a/b) ?
The solution to ln(x/y)-ln(a/b) is ln((bx)/(ay))