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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{3} (6) + lo g_{3} (2)

\frac{3}{2} (ln (x^{2} - 1) - ln (x + 1) + ln (x - 1))

- lo g_{10} (h^{3} o)

- lo g_{10} (6.3 \times 1 0^{- 5})

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