What is 4ln(x)+3ln(y)-5ln(z) ?

The solution to 4ln(x)+3ln(y)-5ln(z) is ln((x^4y^3)/(z^5))

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simplify 4ln(x)+3ln(y)-5ln(z)

simplify

4 ln (x) + 3 ln (y) - 5 ln (z)

ln (\frac{x ^{4} y ^{3}}{z ^{5}})

Solution steps

4 ln (x) + 3 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}) + 3 ln (y) - 5 ln (z)

Apply log rule:

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

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

= ln (x^{4}) + ln (y^{3}) - 5 ln (z)

Apply log rule:

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

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

= ln (x^{4} y^{3}) - 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^{3}) - ln (z^{5})

Apply log rule:

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

ln (x^{4} y^{3}) - ln (z^{5}) = ln (\frac{x ^{4} y ^{3}}{z ^{5}})

= ln (\frac{x ^{4} y ^{3}}{z ^{5}})

ln (\frac{( x + 1 )}{( 1 - x )})

8 ln (x) - \frac{1}{5} ln (y)

lo g_{A} (A \cdot 8^{4})

\frac{1}{3} lo g_{10} (125) - \frac{1}{2} lo g_{10} (64)

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

What is 4ln(x)+3ln(y)-5ln(z) ?
The solution to 4ln(x)+3ln(y)-5ln(z) is ln((x^4y^3)/(z^5))