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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{8} (16 x) + lo g_{8} (2 x^{2})

lo g_{10} (y x^{4})

2 \cdot lo g_{3} (x) + 3 \cdot lo g_{3} (2 y)

f (x) = ln (x^{9}) - ln (x)

ln (\frac{1}{e})

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