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

The solution to ln(sqrt(3u))-ln(sqrt(u)) is 1/2 ln(3)

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

simplify

ln (3 u) - ln (u)

\frac{1}{2} ln (3)

Decimal Notation

0.54930 \dots

Solution steps

ln (3 u) - ln (u)

Apply log rule:

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

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

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

\frac{3 u}{u} = 3

= ln (3)

Rewrite as

= ln (3^{\frac{1}{2}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{2} ln (3)

lo g_{2} (\frac{1}{0.2}) + 1

5 lo g_{5} (a) - 10 lo g_{5} (b)

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

ln (\frac{25}{360 - 25})

5 lo g_{3} (x) + 3 lo g_{3} (y) - 2

What is ln(sqrt(3u))-ln(sqrt(u)) ?
The solution to ln(sqrt(3u))-ln(sqrt(u)) is 1/2 ln(3)