What is ln(((1+(sqrt(3))/2))/(1/2)) ?

The solution to ln(((1+(sqrt(3))/2))/(1/2)) is ln(1+(sqrt(3))/2)+ln(2)

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simplify ln(((1+(sqrt(3))/2))/(1/2))

simplify

ln \frac{( 1 + \frac{3}{2} )}{\frac{1}{2}}

ln (1 + \frac{3}{2}) + ln (2)

Decimal Notation

1.31695 \dots

Solution steps

ln \frac{( 1 + \frac{3}{2} )}{\frac{1}{2}}

Apply log rule:

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

ln \frac{( 1 + \frac{3}{2} )}{\frac{1}{2}} = ln ((1 + \frac{3}{2})) - ln (\frac{1}{2})

= ln (\frac{3}{2} + 1) - ln (\frac{1}{2})

Apply log rule:

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

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

= ln (\frac{3}{2} + 1) - (ln (1) - ln (2))

- (ln (1) - ln (2)) = ln (2)

= ln (\frac{3}{2} + 1) + ln (2)

\frac{d}{d x} (\frac{3}{x}) - ln (b x)

ln ∣ 100 - 3 ∣ - ln ∣ 100 - 2 ∣

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

ln (9 X^{0.3} Y^{0.7})

- lo g_{10} (3.24 \cdot 1 0^{- 11})

What is ln(((1+(sqrt(3))/2))/(1/2)) ?
The solution to ln(((1+(sqrt(3))/2))/(1/2)) is ln(1+(sqrt(3))/2)+ln(2)