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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

ln (\frac{1}{2 t ^{3 n}})

ln (\frac{2}{2})

lo g_{10} (5 \cdot 1 0^{- 6})

ln (x - 8) - ln (17)

\frac{2}{3} ln (5 \cdot 2)

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