What is ln(x)-6ln(y)+ln(z) ?

The solution to ln(x)-6ln(y)+ln(z) is ln((xz)/(y^6))

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simplify ln(x)-6ln(y)+ln(z)

simplify

ln (x) - 6 ln (y) + ln (z)

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

Solution steps

ln (x) - 6 ln (y) + ln (z)

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

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

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

8 = \frac{z}{6}

5 x^{2} + 22 x - 120 = 12 x

E, y^{2} - 2 y E - x^{2} + 2 x E \leq 0

4 k^{2} + 7 jk - 2 j^{2}

\frac{8 x + 7}{6} + \frac{3 - 2 x}{4} - \frac{5 x - 2}{2} = 32

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