What is 3ln(x)+4ln(yz)-ln(x^3y^2) ?

The solution to 3ln(x)+4ln(yz)-ln(x^3y^2) is ln(y^2z^4)

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simplify 3ln(x)+4ln(yz)-ln(x^3y^2)

simplify

3 ln (x) + 4 ln (yz) - ln (x^{3} y^{2})

ln (y^{2} z^{4})

Solution steps

3 ln (x) + 4 ln (yz) - ln (x^{3} y^{2})

Apply log rule:

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

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

= ln (x^{3}) + 4 ln (yz) - ln (x^{3} y^{2})

Apply log rule:

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

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

= ln (x^{3}) + ln ((yz)^{4}) - ln (x^{3} y^{2})

Apply log rule:

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

ln (x^{3}) + ln ((yz)^{4}) = ln (x^{3} (yz)^{4})

= ln (x^{3} (yz)^{4}) - ln (x^{3} y^{2})

(yz)^{4} = y^{4} z^{4}

= ln (x^{3} y^{4} z^{4}) - ln (x^{3} y^{2})

Apply log rule:

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

ln (x^{3} y^{4} z^{4}) - ln (x^{3} y^{2}) = ln (\frac{x ^{3} y ^{4} z ^{4}}{x ^{3} y ^{2}})

= ln (\frac{x ^{3} y ^{4} z ^{4}}{x ^{3} y ^{2}})

Simplify

\frac{x ^{3} y ^{4} z ^{4}}{x ^{3} y ^{2}} : y^{2} z^{4}

= ln (y^{2} z^{4})

lo g_{8} (\frac{1}{6})

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

ln (\frac{3 y}{x ^{5}})

ln (x^{2} - 25) - ln (x + 5)

lo g_{10} (\frac{1}{20})

What is 3ln(x)+4ln(yz)-ln(x^3y^2) ?
The solution to 3ln(x)+4ln(yz)-ln(x^3y^2) is ln(y^2z^4)