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Popular >

simplify ln(x)-ln(y)+ln(z)

Solution

simplify

ln (x) - ln (y) + ln (z)

Solution

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

Solution steps

ln (x) - ln (y) + ln (z)

Apply log rule:

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

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

= ln (\frac{x}{y}) + ln (z)

Apply log rule:

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

ln (\frac{x}{y}) + ln (z) = ln (\frac{x}{y} z)

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

Multiply fractions:

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

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

Popular Examples

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Frequently Asked Questions (FAQ)

What is ln(x)-ln(y)+ln(z) ?
The solution to ln(x)-ln(y)+ln(z) is ln((xz)/y)