What is 4ln(x)+6ln(y)-5ln(z) ?

The solution to 4ln(x)+6ln(y)-5ln(z) is ln((x^4y^6)/(z^5))

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simplify 4ln(x)+6ln(y)-5ln(z)

simplify

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

ln (\frac{x ^{4} y ^{6}}{z ^{5}})

Solution steps

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

Apply log rule:

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

4 ln (x) = ln (x^{4})

= ln (x^{4}) + 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^{4}) + ln (y^{6}) - 5 ln (z)

Apply log rule:

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

ln (x^{4}) + ln (y^{6}) = ln (x^{4} y^{6})

= ln (x^{4} 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^{4} y^{6}) - ln (z^{5})

Apply log rule:

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

ln (x^{4} y^{6}) - ln (z^{5}) = ln (\frac{x ^{4} y ^{6}}{z ^{5}})

= ln (\frac{x ^{4} y ^{6}}{z ^{5}})

3 π + 16 ln (\frac{2}{2})

\frac{1}{2} lo g_{10} (x) - 3 lo g_{10} (sin (2 x)) + 2

ln (\frac{15625}{2187})

ln (\frac{9}{3})

What is 4ln(x)+6ln(y)-5ln(z) ?
The solution to 4ln(x)+6ln(y)-5ln(z) is ln((x^4y^6)/(z^5))