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Popular >

simplify ln(a)-ln(b)+ln(c)

Solution

simplify

ln (a) - ln (b) + ln (c)

Solution

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

Solution steps

ln (a) - ln (b) + ln (c)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

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

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

Popular Examples

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Frequently Asked Questions (FAQ)

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