What is ln(12)+1/2 ln(x/2)+1/2 ln((x/2)R) ?

The solution to ln(12)+1/2 ln(x/2)+1/2 ln((x/2)R) is ln(6sqrt(2)sqrt((x^2R)/2))

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simplify ln(12)+1/2 ln(x/2)+1/2 ln((x/2)R)

simplify

ln (12) + \frac{1}{2} ln (\frac{x}{2}) + \frac{1}{2} ln ((\frac{x}{2}) R)

ln (62 \frac{x ^{2} R}{2})

Solution steps

ln (12) + \frac{1}{2} ln (\frac{x}{2}) + \frac{1}{2} ln ((\frac{x}{2}) R)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

= ln (12) + ln ((\frac{x}{2})^{\frac{1}{2}}) + \frac{1}{2} ln ((\frac{x}{2}) R)

Apply log rule:

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

ln (12) + ln ((\frac{x}{2})^{\frac{1}{2}}) = ln (12 (\frac{x}{2})^{\frac{1}{2}})

= ln (12 (\frac{x}{2})^{\frac{1}{2}}) + \frac{1}{2} ln (\frac{x}{2} R)

Simplify

12 (\frac{x}{2})^{\frac{1}{2}} : 62 x

= ln (62 x) + \frac{1}{2} ln (\frac{x}{2} R)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

\frac{1}{2} ln (\frac{x}{2} R) = ln ((\frac{x}{2} R)^{\frac{1}{2}})

= ln (62 x) + ln ((\frac{x}{2} R)^{\frac{1}{2}})

Apply log rule:

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

ln (62 x) + ln ((\frac{x}{2} R)^{\frac{1}{2}}) = ln (62 x (\frac{x}{2} R)^{\frac{1}{2}})

= ln (62 x (\frac{x}{2} R)^{\frac{1}{2}})

Simplify

62 x (\frac{x}{2} R)^{\frac{1}{2}} : 62 \frac{x ^{2} R}{2}

= ln (62 \frac{x ^{2} R}{2})

ln (\frac{0.01}{0.05})

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

\frac{2}{3} ln (\frac{3 a}{2 s})

ln (2) + ln (- 2)

What is ln(12)+1/2 ln(x/2)+1/2 ln((x/2)R) ?
The solution to ln(12)+1/2 ln(x/2)+1/2 ln((x/2)R) is ln(6sqrt(2)sqrt((x^2R)/2))