What is 4ln(x)+2ln(y)-5ln(z) ?

The solution to 4ln(x)+2ln(y)-5ln(z) is ln((x^4y^2)/(z^5))

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simplify 4ln(x)+2ln(y)-5ln(z)

simplify

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

ln (\frac{x ^{4} y ^{2}}{z ^{5}})

Solution steps

4 ln (x) + 2 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}) + 2 ln (y) - 5 ln (z)

Apply log rule:

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

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

= ln (x^{4}) + ln (y^{2}) - 5 ln (z)

Apply log rule:

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

ln (x^{4}) + ln (y^{2}) = ln (x^{4} y^{2})

= ln (x^{4} y^{2}) - 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^{2}) - ln (z^{5})

Apply log rule:

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

ln (x^{4} y^{2}) - ln (z^{5}) = ln (\frac{x ^{4} y ^{2}}{z ^{5}})

= ln (\frac{x ^{4} y ^{2}}{z ^{5}})

4 lo g_{3} (x) - \frac{1}{3} lo g_{3} (x + 6)

lo g_{a} (x) + lo g_{a} (y) - lo g_{a} (z)

lo g_{6} (\frac{16 x ^{2}}{2 x - 4})

3 lo g_{10} (2) + lo g_{10} (x) - lo g_{10} (4 x)

lo g_{10} (5 x + 7) - lo g_{10} (x)

What is 4ln(x)+2ln(y)-5ln(z) ?
The solution to 4ln(x)+2ln(y)-5ln(z) is ln((x^4y^2)/(z^5))