What is ln((1-sqrt(1-4x^2))/(2x)) ?

The solution to ln((1-sqrt(1-4x^2))/(2x)) is ln(1-sqrt(1-4x^2))-ln(2)-ln(x)

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simplify ln((1-sqrt(1-4x^2))/(2x))

simplify

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

ln (1 - 1 - 4 x^{2}) - ln (2) - ln (x)

Solution steps

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

Apply log rule:

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

ln (\frac{1 - 1 - 4 x ^{2}}{2 x}) = ln (1 - 1 - 4 x^{2}) - ln (2 x)

= ln (- - 4 x^{2} + 1 + 1) - ln (2 x)

Apply log rule:

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

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

= ln (- - 4 x^{2} + 1 + 1) - (ln (x) + ln (2))

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

= ln (1 - 1 - 4 x^{2}) - ln (2) - ln (x)

- lo g_{10} (1.34 \cdot 1 0^{- 3})

lo g_{3} (4) + lo g_{3} (11)

lo g_{10} (6) + 4 lo g_{10} (2)

- lo g_{10} (1 x 1 0^{- 7})

\frac{1}{4} lo g_{c} (x) + 5 lo g_{c} (y) - 4 lo g_{c} (x)

What is ln((1-sqrt(1-4x^2))/(2x)) ?
The solution to ln((1-sqrt(1-4x^2))/(2x)) is ln(1-sqrt(1-4x^2))-ln(2)-ln(x)