What is simplify-ln(((1/2))/2) ?

The solution to simplify-ln(((1/2))/2) is 2ln(2)

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simplify-ln(((1/2))/2)

simplify

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

2 ln (2)

Decimal Notation

1.38629 \dots

Solution steps

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

Apply log rule:

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

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

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

Remove parentheses:

(a) = a

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

Remove parentheses:

(a) = a

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

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - (- ln (2) - ln (2))

Add similar elements:

- ln (2) - ln (2) = - 2 ln (2)

= - (- 2 ln (2))

Apply rule

- (- a) = a

= 2 ln (2)

\frac{1}{3} lo g_{4} (x) + lo g_{4} (z)

- lo g_{10} (5 x 1 0^{- 4})

3 ln (x) - ln (x + 6) - ln (x - 6)

ln (\frac{R}{0.203})

5 ln (x) + 2 ln (y) + ln (z)

What is simplify-ln(((1/2))/2) ?
The solution to simplify-ln(((1/2))/2) is 2ln(2)