What is 4ln(x)-1/8 ln(y) ?

The solution to 4ln(x)-1/8 ln(y) is ln((x^4y^{7/8})/y)

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simplify 4ln(x)-1/8 ln(y)

simplify

4 ln (x) - \frac{1}{8} ln (y)

ln (\frac{x ^{4} y ^{\frac{7}{8}}}{y})

Solution steps

4 ln (x) - \frac{1}{8} 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}{8} ln (y)

Apply log rule:

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

\frac{1}{8} ln (y) = ln (y^{\frac{1}{8}})

= ln (x^{4}) - ln (y^{\frac{1}{8}})

Apply log rule:

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

ln (x^{4}) - ln (y^{\frac{1}{8}}) = ln (\frac{x ^{4}}{y ^{\frac{1}{8}}})

= ln (\frac{x ^{4}}{y ^{\frac{1}{8}}})

Simplify

\frac{x ^{4}}{y ^{\frac{1}{8}}} : \frac{x ^{4} y ^{\frac{7}{8}}}{y}

= ln (\frac{x ^{4} y ^{\frac{7}{8}}}{y})

lo g_{2} (x) + 5 lo g_{2} (y) - 5 lo g_{2} (z)

lo g_{10} (\frac{x ^{2}}{2})

\frac{1}{2} ln (x + 1) - \frac{1}{4} ln (x^{2} + 1)

5 lo g_{10} (a) - 25 lo g_{10} (b)

What is 4ln(x)-1/8 ln(y) ?
The solution to 4ln(x)-1/8 ln(y) is ln((x^4y^{7/8})/y)