What is ln(sqrt(3x))-ln(sqrt(u)) ?

The solution to ln(sqrt(3x))-ln(sqrt(u)) is ln((sqrt(3)sqrt(x)sqrt(u))/u)

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simplify ln(sqrt(3x))-ln(sqrt(u))

simplify

ln (3 x) - ln (u)

ln (\frac{3 x u}{u})

Solution steps

ln (3 x) - ln (u)

Apply log rule:

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

ln (3 x) - ln (u) = ln (\frac{3 x}{u})

= ln (\frac{3 x}{u})

Simplify

\frac{3 x}{u} : \frac{3 x u}{u}

= ln (\frac{3 x u}{u})

- \frac{1}{4} ln (\frac{1}{3})

ln (2 e^{2 x + 1} x)

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

- lo g_{10} (1.24 \cdot 1 0^{- 4})

ln (3) + 2 ln (5)

What is ln(sqrt(3x))-ln(sqrt(u)) ?
The solution to ln(sqrt(3x))-ln(sqrt(u)) is ln((sqrt(3)sqrt(x)sqrt(u))/u)