What is 4ln(x)-7ln(y)-ln(z) ?

The solution to 4ln(x)-7ln(y)-ln(z) is ln((x^4)/(y^7z))

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simplify 4ln(x)-7ln(y)-ln(z)

simplify

4 ln (x) - 7 ln (y) - ln (z)

ln (\frac{x ^{4}}{y ^{7} z})

Solution steps

4 ln (x) - 7 ln (y) - ln (z)

Apply log rule:

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

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

= ln (x^{4}) - 7 ln (y) - ln (z)

Apply log rule:

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

7 ln (y) = ln (y^{7})

= ln (x^{4}) - ln (y^{7}) - ln (z)

Apply log rule:

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

ln (x^{4}) - ln (y^{7}) = ln (\frac{x ^{4}}{y ^{7}})

= ln (\frac{x ^{4}}{y ^{7}}) - ln (z)

Apply log rule:

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

ln (\frac{x ^{4}}{y ^{7}}) - ln (z) = ln (\frac{\frac{x ^{4}}{y ^{7}}}{z})

= ln (\frac{\frac{x ^{4}}{y ^{7}}}{z})

Apply the fraction rule:

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

= ln (\frac{x ^{4}}{y ^{7} z})

ln (5 x) - ln (5 y)

ln (\frac{9}{91})

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

lo g_{b} (3 b a^{2})

2 ln (2 x) - ln (2 x)

What is 4ln(x)-7ln(y)-ln(z) ?
The solution to 4ln(x)-7ln(y)-ln(z) is ln((x^4)/(y^7z))