What is ln(sin(x)[ pi/4 (3pi)/4 ]) ?

The solution to ln(sin(x)[ pi/4 (3pi)/4 ]) is ln(sin(x))+2ln(pi)-4ln(2)+ln(3)

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Popular >

simplify ln(sin(x)[ pi/4 (3pi)/4 ])

simplify

ln (sin (x) [\frac{π}{4} \frac{3 π}{4}])

ln (sin (x)) + 2 ln (π) - 4 ln (2) + ln (3)

Solution steps

ln (sin (x) [\frac{π}{4} \cdot \frac{3 π}{4}])

Apply log rule:

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

ln (sin (x) [\frac{π}{4} \cdot \frac{3 π}{4}]) = ln (sin (x)) + ln (\frac{π}{4} \cdot \frac{3 π}{4})

= ln (sin (x)) + ln (\frac{π}{4} \cdot \frac{3 π}{4})

Apply log rule:

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

ln (\frac{π}{4} \cdot \frac{3 π}{4}) = ln (\frac{π}{4}) + ln (\frac{3 π}{4})

= ln (sin (x)) + ln (\frac{π}{4}) + ln (\frac{3 π}{4})

Apply log rule:

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

ln (\frac{π}{4}) = ln (π) - ln (4), ln (\frac{3 π}{4}) = ln (3 π) - ln (4)

= ln (sin (x)) + + ln (π) - ln (4) + + ln (3 π) - ln (4)

Simplify

ln (sin (x)) + + ln (π) - ln (4) + + ln (3 π) - ln (4) : ln (sin (x)) + ln (π) - 2 ln (4) + ln (3 π)

Apply log rule:

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

ln (3 π) = ln (3) + ln (π)

= ln (sin (x)) + ln (π) - 2 ln (4) + ln (3) + ln (π)

Add similar elements:

ln (π) + ln (π) = 2 ln (π)

= ln (sin (x)) + 2 ln (π) - 2 ln (4) + ln (3)

2 ln (4) = 4 ln (2)

= ln (sin (x)) + 2 ln (π) - 4 ln (2) + ln (3)

- lo g_{10} (5.63408 \cdot 1 0^{- 6})

lo g_{b} (\frac{A}{b})

4 ln (x) + 7 ln (z)

7 lo g_{b} (x) + 8 lo g_{b} (z)

lo g_{2} (3 c)

What is ln(sin(x)[ pi/4 (3pi)/4 ]) ?
The solution to ln(sin(x)[ pi/4 (3pi)/4 ]) is ln(sin(x))+2ln(pi)-4ln(2)+ln(3)