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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

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

- 5137.521 + 1239.973 ln (\frac{2015}{30})

4 lo g_{c} (2 z + 1) + \frac{1}{5} lo g_{c} (z + 2)

lo g_{1.12} (\frac{125}{12}) + 1

0.3 \cdot ln (3400) + 0.7 \cdot ln (5800)

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