What is simplify-3ln(x)+1/2 ln(y)+ln(z) ?

The solution to simplify-3ln(x)+1/2 ln(y)+ln(z) is ln((zy^{1/2})/(x^3))

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simplify-3ln(x)+1/2 ln(y)+ln(z)

simplify

- 3 ln (x) + \frac{1}{2} ln (y) + ln (z)

ln (\frac{z y ^{\frac{1}{2}}}{x ^{3}})

Solution steps

- 3 ln (x) + \frac{1}{2} ln (y) + ln (z)

Apply log rule:

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

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

= - ln (x^{3}) + \frac{1}{2} ln (y) + ln (z)

Apply log rule:

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

\frac{1}{2} ln (y) = ln (y^{\frac{1}{2}})

= - ln (x^{3}) + ln (y^{\frac{1}{2}}) + ln (z)

Apply log rule:

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

ln (y^{\frac{1}{2}}) - ln (x^{3}) = ln (\frac{y ^{\frac{1}{2}}}{x ^{3}})

= ln (\frac{y ^{\frac{1}{2}}}{x ^{3}}) + ln (z)

Apply log rule:

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

ln (\frac{y ^{\frac{1}{2}}}{x ^{3}}) + ln (z) = ln (\frac{y ^{\frac{1}{2}}}{x ^{3}} z)

= ln (\frac{y ^{\frac{1}{2}}}{x ^{3}} z)

Multiply fractions:

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

= ln (\frac{z y ^{\frac{1}{2}}}{x ^{3}})

4 lo g_{2} (c) - 8 lo g_{2} (n)

ln (\frac{- x ^{6}}{y ^{6}})

- (\frac{5}{6}) \cdot lo g_{2} (\frac{5}{6}) - (\frac{1}{6}) \cdot lo g_{2} (\frac{1}{6})

2 ln (8) + 3 ln (z)

0.78 - \frac{0.05916}{4} lo g_{10} (\frac{1}{( \frac{1}{x} ) ^{2}})

What is simplify-3ln(x)+1/2 ln(y)+ln(z) ?
The solution to simplify-3ln(x)+1/2 ln(y)+ln(z) is ln((zy^{1/2})/(x^3))