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Popular >

simplify ln((a/c)/(b/d))+ln(c/d)

Solution

simplify

ln (\frac{\frac{a}{c}}{\frac{b}{d}}) + ln (\frac{c}{d})

Solution

ln (\frac{a}{b})

Solution steps

ln (\frac{\frac{a}{c}}{\frac{b}{d}}) + ln (\frac{c}{d})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{\frac{a}{c}}{\frac{b}{d}}) + ln (\frac{c}{d}) = ln (\frac{c}{d} \cdot \frac{\frac{a}{c}}{\frac{b}{d}})

= ln (\frac{c}{d} \cdot \frac{\frac{a}{c}}{\frac{b}{d}})

Simplify

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

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

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Frequently Asked Questions (FAQ)

What is ln((a/c)/(b/d))+ln(c/d) ?
The solution to ln((a/c)/(b/d))+ln(c/d) is ln(a/b)