What is ln((sqrt(x))/(y^6)) ?

The solution to ln((sqrt(x))/(y^6)) is ln(sqrt(x))-6ln(y)

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simplify ln((sqrt(x))/(y^6))

simplify

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

ln (x) - 6 ln (y)

Solution steps

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

Apply log rule:

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

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

= ln (x) - ln (y^{6})

Apply log rule:

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

ln (y^{6}) = 6 ln (y)

= ln (x) - 6 ln (y)

- lo g_{10} (x \cdot 1 0^{- n})

\frac{( ln ( x ) - ln ( y ) )}{x}

- lo g_{10} (0.39 \cdot 1 0^{- 3})

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

- lo g_{10} (4.12 \cdot 1 0^{- 3})

What is ln((sqrt(x))/(y^6)) ?
The solution to ln((sqrt(x))/(y^6)) is ln(sqrt(x))-6ln(y)