What is 2ln(x)+ln(y)-ln(z+4) ?

The solution to 2ln(x)+ln(y)-ln(z+4) is ln((x^2y)/(z+4))

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simplify 2ln(x)+ln(y)-ln(z+4)

simplify

2 ln (x) + ln (y) - ln (z + 4)

ln (\frac{x ^{2} y}{z + 4})

Solution steps

2 ln (x) + ln (y) - ln (z + 4)

Apply log rule:

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

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

= ln (x^{2}) + ln (y) - ln (z + 4)

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) - ln (z + 4)

Apply log rule:

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

ln (x^{2} y) - ln (z + 4) = ln (\frac{x ^{2} y}{z + 4})

= ln (\frac{x ^{2} y}{z + 4})

ln (20 e)

- lo g_{10} (6 \cdot 1 0^{- 9})

lo g_{10} (2) + lo g_{10} (x + 3)

lo g_{10} (\frac{a b ^{2}}{m})

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

What is 2ln(x)+ln(y)-ln(z+4) ?
The solution to 2ln(x)+ln(y)-ln(z+4) is ln((x^2y)/(z+4))