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Popular >

simplify ln((12x)/(4x))

Solution

simplify

ln (\frac{12 x}{4 x})

Solution

- 2 ln (2) + ln (12)

+1

Solution steps

ln (\frac{12 x}{4 x})

Apply log rule:

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

ln (\frac{12 x}{4 x}) = ln (12 x) - ln (4 x)

= ln (12 x) - ln (4 x)

Apply log rule:

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

ln (12 x) = ln (12) + ln (x), ln (4 x) = ln (4) + ln (x)

= ln (12) + ln (x) - (ln (x) + ln (4))

ln (4) = 2 ln (2)

= ln (12) + ln (x) - (ln (x) + 2 ln (2))

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

= ln (12) + ln (x) - 2 ln (2) - ln (x)

Simplify

ln (12) + ln (x) - 2 ln (2) - ln (x) : - 2 ln (2) + ln (12)

= - 2 ln (2) + ln (12)

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Frequently Asked Questions (FAQ)

What is ln((12x)/(4x)) ?
The solution to ln((12x)/(4x)) is -2ln(2)+ln(12)