What is 4ln(x)-5ln(y)-6ln(z) ?

The solution to 4ln(x)-5ln(y)-6ln(z) is ln((x^4)/(y^5z^6))

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simplify 4ln(x)-5ln(y)-6ln(z)

simplify

4 ln (x) - 5 ln (y) - 6 ln (z)

ln (\frac{x ^{4}}{y ^{5} z ^{6}})

Solution steps

4 ln (x) - 5 ln (y) - 6 ln (z)

Apply log rule:

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

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

= ln (x^{4}) - 5 ln (y) - 6 ln (z)

Apply log rule:

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

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

= ln (x^{4}) - ln (y^{5}) - 6 ln (z)

Apply log rule:

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

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

= ln (\frac{x ^{4}}{y ^{5}}) - 6 ln (z)

Apply log rule:

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

6 ln (z) = ln (z^{6})

= ln (\frac{x ^{4}}{y ^{5}}) - ln (z^{6})

Apply log rule:

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

ln (\frac{x ^{4}}{y ^{5}}) - ln (z^{6}) = ln (\frac{\frac{x ^{4}}{y ^{5}}}{z ^{6}})

= ln (\frac{\frac{x ^{4}}{y ^{5}}}{z ^{6}})

Apply the fraction rule:

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

= ln (\frac{x ^{4}}{y ^{5} z ^{6}})

- (\frac{3}{5} lo g_{2} (\frac{3}{5}) + \frac{2}{5} lo g_{2} (\frac{2}{5}))

ln (2.89755 \cdot 1 0^{50})

lo g_{b} (\frac{x ^{2}}{y ^{2} z ^{3}})

lo g_{10} (x) - \frac{1}{4} lo g_{10} (y) + 4 lo g_{10} (z)

lo g_{10} (4 x^{5})

What is 4ln(x)-5ln(y)-6ln(z) ?
The solution to 4ln(x)-5ln(y)-6ln(z) is ln((x^4)/(y^5z^6))