What is ln((sqrt(x))/(y^4)) ?

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

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simplify ln((sqrt(x))/(y^4))

simplify

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

ln (x) - 4 ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= ln (x) - 4 ln (y)

3 lo g_{a} (x) + 4 lo g_{a} (y)

- lo g_{10} (4 x 1 0^{- 3})

\frac{1}{3} ln (11)

ln (- 2.5 \cdot 1 0^{23})

ln (x^{6} e^{- 6 x})

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