What is 3ln(x)+6ln(y)-4ln(z) ?

The solution to 3ln(x)+6ln(y)-4ln(z) is ln((x^3y^6)/(z^4))

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simplify 3ln(x)+6ln(y)-4ln(z)

simplify

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

ln (\frac{x ^{3} y ^{6}}{z ^{4}})

Solution steps

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

Apply log rule:

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

3 ln (x) = ln (x^{3})

= ln (x^{3}) + 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^{3}) + ln (y^{6}) - 4 ln (z)

Apply log rule:

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

ln (x^{3}) + ln (y^{6}) = ln (x^{3} y^{6})

= ln (x^{3} 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^{3} y^{6}) - ln (z^{4})

Apply log rule:

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

ln (x^{3} y^{6}) - ln (z^{4}) = ln (\frac{x ^{3} y ^{6}}{z ^{4}})

= ln (\frac{x ^{3} y ^{6}}{z ^{4}})

4 ln (x) - \frac{1}{4} ln (y)

lo g_{2} (\frac{8}{x + 7})

lo g_{2} (2 x + 1) - 5 lo g_{4} (x^{2}) + 4 lo g_{2} (x)

lo g_{3} ((\frac{3}{x})^{3})

lo g_{10} (3 \cdot 1 0^{x})

What is 3ln(x)+6ln(y)-4ln(z) ?
The solution to 3ln(x)+6ln(y)-4ln(z) is ln((x^3y^6)/(z^4))