What is 2ln(x)-3ln(y)+5ln(z) ?

The solution to 2ln(x)-3ln(y)+5ln(z) is ln((x^2z^5)/(y^3))

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simplify 2ln(x)-3ln(y)+5ln(z)

simplify

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

ln (\frac{x ^{2} z ^{5}}{y ^{3}})

Solution steps

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

Apply log rule:

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

2 ln (x) = ln (x^{2})

= ln (x^{2}) - 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^{2}) - ln (y^{3}) + 5 ln (z)

Apply log rule:

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

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

= ln (\frac{x ^{2}}{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 (\frac{x ^{2}}{y ^{3}}) + ln (z^{5})

Apply log rule:

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

ln (\frac{x ^{2}}{y ^{3}}) + ln (z^{5}) = ln (\frac{x ^{2}}{y ^{3}} z^{5})

= ln (\frac{x ^{2}}{y ^{3}} z^{5})

Multiply fractions:

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

= ln (\frac{x ^{2} z ^{5}}{y ^{3}})

lo g_{3} (x^{2} + 9 x + 18) - lo g_{3} (x + 3)

\frac{2}{3} lo g_{10} (\frac{5.96 x ^{1016}}{1 0 ^{4.4}})

lo g_{2} (\frac{x}{500})

ln (\frac{e ^{7}}{9})

4 lo g_{5} (x) + lo g_{5} (y)

What is 2ln(x)-3ln(y)+5ln(z) ?
The solution to 2ln(x)-3ln(y)+5ln(z) is ln((x^2z^5)/(y^3))