What is ln(x)+2ln(y+1)-1/2 ln(z) ?

The solution to ln(x)+2ln(y+1)-1/2 ln(z) is ln((xsqrt(z)(y+1)^2)/z)

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simplify ln(x)+2ln(y+1)-1/2 ln(z)

simplify

ln (x) + 2 ln (y + 1) - \frac{1}{2} ln (z)

ln (\frac{x z ( y + 1 ) ^{2}}{z})

Solution steps

ln (x) + 2 ln (y + 1) - \frac{1}{2} ln (z)

Apply log rule:

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

2 ln (y + 1) = ln ((y + 1)^{2})

= ln (x) + ln ((y + 1)^{2}) - \frac{1}{2} ln (z)

Apply log rule:

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

ln (x) + ln ((y + 1)^{2}) = ln (x (y + 1)^{2})

= ln (x (y + 1)^{2}) - \frac{1}{2} ln (z)

Apply log rule:

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

\frac{1}{2} ln (z) = ln (z^{\frac{1}{2}})

= ln (x (y + 1)^{2}) - ln (z^{\frac{1}{2}})

Apply log rule:

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

ln (x (y + 1)^{2}) - ln (z^{\frac{1}{2}}) = ln (\frac{x ( y + 1 ) ^{2}}{z ^{\frac{1}{2}}})

= ln (\frac{x ( y + 1 ) ^{2}}{z ^{\frac{1}{2}}})

Simplify

\frac{x ( y + 1 ) ^{2}}{z ^{\frac{1}{2}}} : \frac{x z ( y + 1 ) ^{2}}{z}

= ln (\frac{x z ( y + 1 ) ^{2}}{z})

3 ln ∣ 5 ∣ - 3 ln ∣ 2 ∣

ln (2 u)

lo g_{7} (\frac{9 x ^{2}}{y ^{3}})

lo g_{b} (x^{3} z)

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

What is ln(x)+2ln(y+1)-1/2 ln(z) ?
The solution to ln(x)+2ln(y+1)-1/2 ln(z) is ln((xsqrt(z)(y+1)^2)/z)