What is ln(x/(x/2)) ?

The solution to ln(x/(x/2)) is ln(2)

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simplify ln(x/(x/2))

simplify

ln (\frac{x}{\frac{x}{2}})

ln (2)

Decimal Notation

0.69314 \dots

Solution steps

ln (\frac{x}{\frac{x}{2}})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- (ln (x) - ln (2)) : - ln (x) + ln (2)

= ln (x) - ln (x) + ln (2)

Add similar elements:

ln (x) - ln (x) = 0

= ln (2)

ln (\frac{20474}{375}) \cdot 4

10 lo g_{10} (\frac{\frac{2}{π}}{1 0 ^{- 12}})

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

2 ln (4) - 2 ln (\frac{1}{2})

lo g_{2} (a + b) + lo g_{2} (a - b) - 2 lo g_{2} (a)