What is 4ln(x)+7ln(y)-3ln(z) ?

The solution to 4ln(x)+7ln(y)-3ln(z) is ln((x^4y^7)/(z^3))

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simplify 4ln(x)+7ln(y)-3ln(z)

simplify

4 ln (x) + 7 ln (y) - 3 ln (z)

ln (\frac{x ^{4} y ^{7}}{z ^{3}})

Solution steps

4 ln (x) + 7 ln (y) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{4}) + 7 ln (y) - 3 ln (z)

Apply log rule:

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

7 ln (y) = ln (y^{7})

= ln (x^{4}) + ln (y^{7}) - 3 ln (z)

Apply log rule:

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

ln (x^{4}) + ln (y^{7}) = ln (x^{4} y^{7})

= ln (x^{4} y^{7}) - 3 ln (z)

Apply log rule:

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

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

= ln (x^{4} y^{7}) - ln (z^{3})

Apply log rule:

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

ln (x^{4} y^{7}) - ln (z^{3}) = ln (\frac{x ^{4} y ^{7}}{z ^{3}})

= ln (\frac{x ^{4} y ^{7}}{z ^{3}})

lo g_{10} (\frac{11 x ^{3} y}{z + 1})

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

lo g_{6} (x y)

ln (\frac{4}{9})

ln (x + 2) - ln (x + 1)

What is 4ln(x)+7ln(y)-3ln(z) ?
The solution to 4ln(x)+7ln(y)-3ln(z) is ln((x^4y^7)/(z^3))