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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

5 ln (y) = ln (y^{5})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (14 x y)

\frac{lo g _{10} ( 4 )}{lo g _{10} ( 5 ) - lo g _{10} ( 4 )}

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

10 lo g_{10} (\frac{I}{1 0 ^{- 12}})

lo g_{10} (x) + lo g_{10} (24) - lo g_{10} (2)

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