What is simplify-ln((pid)/4) ?

The solution to simplify-ln((pid)/4) is -ln(pid)+2ln(2)

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simplify-ln((pid)/4)

simplify

- ln (\frac{π d}{4})

- ln (π d) + 2 ln (2)

Solution steps

- ln (\frac{π d}{4})

Apply log rule:

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

ln (\frac{π d}{4}) = ln (π d) - ln (4)

= - (ln (π d) - ln (4))

ln (4) = 2 ln (2)

= - (ln (π d) - 2 ln (2))

Distribute parentheses

= - (ln (π d)) - (- 2 ln (2))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - ln (π d) + 2 ln (2)

ln (\frac{2 ^{- 1}}{3 ^{4} 5 ^{1}})

- lo g_{10} (1.3 \cdot 1 0^{- 12})

2 ln (3) - 2 ln (\frac{5}{3})

ln (y) + ln (x^{2})

ln (\frac{1.6}{0.277})

What is simplify-ln((pid)/4) ?
The solution to simplify-ln((pid)/4) is -ln(pid)+2ln(2)