What is simplify-1/5 ln(x)-5[ln(y)-3ln(z)] ?

The solution to simplify-1/5 ln(x)-5[ln(y)-3ln(z)] is -1/5 ln(x)-5ln(y/(z^3))

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simplify-1/5 ln(x)-5[ln(y)-3ln(z)]

simplify

- \frac{1}{5} ln (x) - 5 [ln (y) - 3 ln (z)]

- \frac{1}{5} ln (x) - 5 ln (\frac{y}{z ^{3}})

Solution steps

- \frac{1}{5} ln (x) - 5 [ln (y) - 3 ln (z)]

Apply log rule:

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

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

= - \frac{1}{5} ln (x) - 5 [ln (y) - ln (z^{3})]

Apply log rule:

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

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

= - \frac{1}{5} ln (x) - 5 [ln (\frac{y}{z ^{3}})]

Remove parentheses:

(a) = a

= - \frac{1}{5} ln (x) - 5 ln (\frac{y}{z ^{3}})

\frac{30 ln ( \frac{25}{114} )}{ln ( \frac{79}{114} )}

lo g_{2} (\frac{1}{1000})

ln (\frac{5}{2}) - \frac{117}{250}

1.97 - \frac{0.0592}{2} lo g_{10} (\frac{800}{16})

ln (5) + 3 ln (4)

What is simplify-1/5 ln(x)-5[ln(y)-3ln(z)] ?
The solution to simplify-1/5 ln(x)-5[ln(y)-3ln(z)] is -1/5 ln(x)-5ln(y/(z^3))