What is 4ln(x)-1/6 ln(y) ?

The solution to 4ln(x)-1/6 ln(y) is ln((x^4y^{5/6})/y)

Popular >

simplify 4ln(x)-1/6 ln(y)

simplify

4 ln (x) - \frac{1}{6} ln (y)

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

Solution steps

4 ln (x) - \frac{1}{6} ln (y)

Apply log rule:

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

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

= ln (x^{4}) - \frac{1}{6} ln (y)

Apply log rule:

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

\frac{1}{6} ln (y) = ln (y^{\frac{1}{6}})

= ln (x^{4}) - ln (y^{\frac{1}{6}})

Apply log rule:

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

ln (x^{4}) - ln (y^{\frac{1}{6}}) = ln (\frac{x ^{4}}{y ^{\frac{1}{6}}})

= ln (\frac{x ^{4}}{y ^{\frac{1}{6}}})

Simplify

\frac{x ^{4}}{y ^{\frac{1}{6}}} : \frac{x ^{4} y ^{\frac{5}{6}}}{y}

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

lo g_{10} (32 x)

ln (\frac{1}{1.7})

25 lo g_{6} (x) + 5 lo g_{6} (y)

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

3 (lo g_{5} (x) + 3 lo g_{5} (y) - 5 lo g_{5} (z))

What is 4ln(x)-1/6 ln(y) ?
The solution to 4ln(x)-1/6 ln(y) is ln((x^4y^{5/6})/y)