What is 2ln(x)-1/8 ln(y) ?

The solution to 2ln(x)-1/8 ln(y) is ln((x^2y^{7/8})/y)

Popular >

simplify 2ln(x)-1/8 ln(y)

simplify

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

ln (\frac{x ^{2} y ^{\frac{7}{8}}}{y})

Solution steps

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

Apply log rule:

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

2 ln (x) = ln (x^{2})

= ln (x^{2}) - \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^{2}) - ln (y^{\frac{1}{8}})

Apply log rule:

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

ln (x^{2}) - ln (y^{\frac{1}{8}}) = ln (\frac{x ^{2}}{y ^{\frac{1}{8}}})

= ln (\frac{x ^{2}}{y ^{\frac{1}{8}}})

Simplify

\frac{x ^{2}}{y ^{\frac{1}{8}}} : \frac{x ^{2} y ^{\frac{7}{8}}}{y}

= ln (\frac{x ^{2} y ^{\frac{7}{8}}}{y})

5 \cdot lo g_{10} (a) + \frac{1}{2} \cdot lo g_{10} (b) - 4 \cdot lo g_{10} (c)

\frac{ln ( x + h ) - ln ( x )}{h}

lo g_{10} (m) + lo g_{10} (n)

lo g_{10} (\frac{x}{5})

ln (14) - ln (7)

What is 2ln(x)-1/8 ln(y) ?
The solution to 2ln(x)-1/8 ln(y) is ln((x^2y^{7/8})/y)