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Popular >

simplify ln((x+1)/(4x))

Solution

simplify

ln (\frac{x + 1}{4 x})

Solution

ln (x + 1) - 2 ln (2) - ln (x)

Solution steps

ln (\frac{x + 1}{4 x})

Apply log rule:

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

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

= ln (x + 1) - ln (4 x)

Apply log rule:

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

ln (4 x) = ln (4) + ln (x)

= ln (x + 1) - (ln (x) + ln (4))

ln (4) = 2 ln (2)

= ln (x + 1) - (ln (x) + 2 ln (2))

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

= ln (x + 1) - 2 ln (2) - ln (x)

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Frequently Asked Questions (FAQ)

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