What is 2ln(x)+ln(y)-0.5ln(z) ?

The solution to 2ln(x)+ln(y)-0.5ln(z) is ln((x^2y)/(z^{0.5)})

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simplify 2ln(x)+ln(y)-0.5ln(z)

simplify

2 ln (x) + ln (y) - 0.5 ln (z)

ln (\frac{x ^{2} y}{z ^{0.5}})

Solution steps

2 ln (x) + ln (y) - 0.5 ln (z)

Apply log rule:

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

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

= ln (x^{2}) + ln (y) - 0.5 ln (z)

Apply log rule:

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

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

= ln (x^{2} y) - 0.5 ln (z)

Apply log rule:

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

0.5 ln (z) = ln (z^{0.5})

= ln (x^{2} y) - ln (z^{0.5})

Apply log rule:

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

ln (x^{2} y) - ln (z^{0.5}) = ln (\frac{x ^{2} y}{z ^{0.5}})

= ln (\frac{x ^{2} y}{z ^{0.5}})

ln (\frac{( x + 4 ) ^{7}}{x ^{7} x + 5})

30 lo g_{6} (3) + 30 lo g_{6} (2) - 6 lo g_{6} (11)

lo g_{b} (x yz) - 2 lo g_{b} (w)

lo g_{4} (6) + 3 lo g_{4} (x)

ln (\frac{1 ^{4}}{( 1 + 1 ) ^{4}})

What is 2ln(x)+ln(y)-0.5ln(z) ?
The solution to 2ln(x)+ln(y)-0.5ln(z) is ln((x^2y)/(z^{0.5)})