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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{2} (k^{2} - 4) - lo g_{2} (k) - 2

2 lo g_{2} (x + 1) - lo g_{2} (x + 3) - lo g_{2} (x - 1)

\frac{1}{3} ln (2)

ln (a \cdot b)

- lo g_{10} (1.3 \cdot 1 0^{- 4})

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