What is ln(sec(pi/3))+1+ln(c)+ln(pi/4) ?

The solution to ln(sec(pi/3))+1+ln(c)+ln(pi/4) is ln((pic)/2)+1

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simplify ln(sec(pi/3))+1+ln(c)+ln(pi/4)

simplify

ln (sec (\frac{π}{3})) + 1 + ln (c) + ln (\frac{π}{4})

ln (\frac{π c}{2}) + 1

Solution steps

ln (sec (\frac{π}{3})) + 1 + ln (c) + ln (\frac{π}{4})

Apply log rule:

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

ln (sec (\frac{π}{3})) + ln (c) = ln (sec (\frac{π}{3}) c)

= ln (sec (\frac{π}{3}) c) + 1 + ln (\frac{π}{4})

Simplify

sec (\frac{π}{3}) : 2

= ln (2 c) + 1 + ln (\frac{π}{4})

Apply log rule:

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

ln (2 c) + ln (\frac{π}{4}) = ln (2 \cdot \frac{π}{4} c)

= ln (2 \cdot \frac{π}{4} c) + 1

Simplify

2 c \frac{π}{4} : \frac{π c}{2}

= ln (\frac{π c}{2}) + 1

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

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

ln ∣ vx ∣ - ln ∣ v ∣

ln (\frac{4}{x + 1}) + ln (x)

ln (\frac{4 + 2 2}{4 - 2 2})

What is ln(sec(pi/3))+1+ln(c)+ln(pi/4) ?
The solution to ln(sec(pi/3))+1+ln(c)+ln(pi/4) is ln((pic)/2)+1