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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

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

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

\frac{1}{3} lo g_{10} (a) - \frac{1}{2} (lo g_{10} (b) - lo g_{10} (c))

lo g_{2} (6) - lo g_{2} (15) - lo g_{2} (20)

lo g_{10} (4 x)

\frac{1}{2} + ln (\frac{1}{2})

lo g_{b} (m) + lo g_{b} (n)

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