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Popular >

simplify ln(2x)-2ln(y)+ln(z)

Solution

simplify

ln (2 x) - 2 ln (y) + ln (z)

Solution

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

Solution steps

ln (2 x) - 2 ln (y) + ln (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (y) = ln (y^{2})

= ln (2 x) - ln (y^{2}) + ln (z)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

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

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

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Frequently Asked Questions (FAQ)

What is ln(2x)-2ln(y)+ln(z) ?
The solution to ln(2x)-2ln(y)+ln(z) is ln((2xz)/(y^2))