What is 2ln(x)+5ln(y)-3ln(z) ?

The solution to 2ln(x)+5ln(y)-3ln(z) is ln((x^2y^5)/(z^3))

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simplify 2ln(x)+5ln(y)-3ln(z)

simplify

2 ln (x) + 5 ln (y) - 3 ln (z)

ln (\frac{x ^{2} y ^{5}}{z ^{3}})

Solution steps

2 ln (x) + 5 ln (y) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{2}) + 5 ln (y) - 3 ln (z)

Apply log rule:

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

5 ln (y) = ln (y^{5})

= ln (x^{2}) + ln (y^{5}) - 3 ln (z)

Apply log rule:

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

ln (x^{2}) + ln (y^{5}) = ln (x^{2} y^{5})

= ln (x^{2} y^{5}) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{2} y^{5}) - ln (z^{3})

Apply log rule:

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

ln (x^{2} y^{5}) - ln (z^{3}) = ln (\frac{x ^{2} y ^{5}}{z ^{3}})

= ln (\frac{x ^{2} y ^{5}}{z ^{3}})

4 ln (3 cos (x))

lo g_{10} (y z^{12})

- lo g_{10} (7.5 \cdot 1 0^{- 4})

2 lo g_{b} (4) + lo g_{b} (5)

lo g_{10} (\frac{z ^{3} y ^{2}}{x})

What is 2ln(x)+5ln(y)-3ln(z) ?
The solution to 2ln(x)+5ln(y)-3ln(z) is ln((x^2y^5)/(z^3))