What is ln(2x)-2ln(y)+ln(z) ?

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

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

simplify

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

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}})

ln (\frac{5 x}{y ^{2}})

ln (y) - ln (c) - ln (x)

ln (1 + x^{2}) - ln (x)

3 ln (x) + 2 ln (y)

ln (\frac{2}{1 - 0 - ( - 1 )})

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