What is 2ln(x)+3ln(y)-ln(z) ?

The solution to 2ln(x)+3ln(y)-ln(z) is ln((x^2y^3)/z)

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simplify 2ln(x)+3ln(y)-ln(z)

simplify

2 ln (x) + 3 ln (y) - ln (z)

ln (\frac{x ^{2} y ^{3}}{z})

Solution steps

2 ln (x) + 3 ln (y) - ln (z)

Apply log rule:

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

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

= ln (x^{2}) + 3 ln (y) - ln (z)

Apply log rule:

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

3 ln (y) = ln (y^{3})

= ln (x^{2}) + ln (y^{3}) - ln (z)

Apply log rule:

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

ln (x^{2}) + ln (y^{3}) = ln (x^{2} y^{3})

= ln (x^{2} y^{3}) - ln (z)

Apply log rule:

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

ln (x^{2} y^{3}) - ln (z) = ln (\frac{x ^{2} y ^{3}}{z})

= ln (\frac{x ^{2} y ^{3}}{z})

7 ln (x) - \frac{1}{3} ln (y)

ln (x^{6} 7 - x)

- lo g_{10} (7.9 \cdot 1 0^{- 9})

lo g_{2} (x y) - \frac{1}{3} lo g_{2} (x^{2})

f (x) = ln (\frac{3 ^{x} 6 ^{3 x}}{2 ^{3 x}})

What is 2ln(x)+3ln(y)-ln(z) ?
The solution to 2ln(x)+3ln(y)-ln(z) is ln((x^2y^3)/z)