What is ln((r*sqrt(0.04))/(2.51)) ?

The solution to ln((r*sqrt(0.04))/(2.51)) is ln(r)+1/2 ln(0.04)-ln(2.51)

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simplify ln((r*sqrt(0.04))/(2.51))

simplify

ln (\frac{r \cdot 0.04}{2.51})

ln (r) + \frac{1}{2} ln (0.04) - ln (2.51)

Solution steps

ln (\frac{r 0.04}{2.51})

Apply log rule:

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

ln (\frac{r 0.04}{2.51}) = ln (r 0.04) - ln (2.51)

= ln (0.04 r) - ln (2.51)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (r 0.04) = ln (r) + ln (0.04)

= ln (r) + ln (0.04) - ln (2.51)

ln (0.04) = \frac{1}{2} ln (0.04)

= ln (r) + \frac{1}{2} ln (0.04) - ln (2.51)

3 lo g_{5} (a) - 3 lo g_{5} (b)

\frac{1}{2} ln (a) + 2 ln (c)

\frac{14 \cdot 0.89}{0.58} \cdot ln (\frac{1}{1 - 0.1})

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

lo g_{e} (4 e^{3 x})

What is ln((r*sqrt(0.04))/(2.51)) ?
The solution to ln((r*sqrt(0.04))/(2.51)) is ln(r)+1/2 ln(0.04)-ln(2.51)