What is 6ln(x)+5ln(y)-2ln(z) ?

The solution to 6ln(x)+5ln(y)-2ln(z) is ln((x^6y^5)/(z^2))

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simplify 6ln(x)+5ln(y)-2ln(z)

simplify

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

ln (\frac{x ^{6} y ^{5}}{z ^{2}})

Solution steps

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

Apply log rule:

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

6 ln (x) = ln (x^{6})

= ln (x^{6}) + 5 ln (y) - 2 ln (z)

Apply log rule:

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

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

= ln (x^{6}) + ln (y^{5}) - 2 ln (z)

Apply log rule:

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

ln (x^{6}) + ln (y^{5}) = ln (x^{6} y^{5})

= ln (x^{6} y^{5}) - 2 ln (z)

Apply log rule:

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

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

= ln (x^{6} y^{5}) - ln (z^{2})

Apply log rule:

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

ln (x^{6} y^{5}) - ln (z^{2}) = ln (\frac{x ^{6} y ^{5}}{z ^{2}})

= ln (\frac{x ^{6} y ^{5}}{z ^{2}})

lo g_{8} (x) + 3 lo g_{8} (2 x - 5) - 7 lo g_{8} (x - 3)

ln (\frac{e ^{x} ln ( 3 )}{3})

- lo g_{10} (7.5 \cdot 1 0^{- 3})

- lo g_{10} (4.3 \cdot 1 0^{- 7})

- \frac{5}{6} lo g_{2} (\frac{5}{6}) - \frac{1}{6} lo g_{2} (\frac{1}{6})

What is 6ln(x)+5ln(y)-2ln(z) ?
The solution to 6ln(x)+5ln(y)-2ln(z) is ln((x^6y^5)/(z^2))