What is ln((sqrt(x^2))/(sqrt(y^5))) ?

The solution to ln((sqrt(x^2))/(sqrt(y^5))) is ln(sqrt(x^2))-ln(sqrt(y)sqrt(y^4))

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simplify ln((sqrt(x^2))/(sqrt(y^5)))

simplify

ln (\frac{x ^{2}}{y ^{5}})

ln (x^{2}) - ln (y y^{4})

Solution steps

ln (\frac{x ^{2}}{y ^{5}})

Apply log rule:

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

ln (\frac{x ^{2}}{y ^{5}}) = ln (x^{2}) - ln (y^{5})

= ln (x^{2}) - ln (y^{5})

y^{5} = y y^{4}

= ln (x^{2}) - ln (y y^{4})

lo g_{e} (4) - lo g_{e} (2) - lo g_{e} (3)

ln (13) - ln (12)

2.12 - \frac{0.0592}{2} \cdot lo g_{10} (\frac{0.4}{0.6})

3 lo g_{10} (a) - 4 lo g_{10} (y)

4 ln (\frac{y}{x}) + 4 ln (x)

What is ln((sqrt(x^2))/(sqrt(y^5))) ?
The solution to ln((sqrt(x^2))/(sqrt(y^5))) is ln(sqrt(x^2))-ln(sqrt(y)sqrt(y^4))