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Popular >

simplify 2ln|x|-ln|x-3|

Solution

simplify

2 ln ∣ x ∣ - ln ∣ x - 3 ∣

Solution

ln (\frac{x ^{2}}{∣ x - 3 ∣})

Solution steps

2 ln ∣ x ∣ - ln ∣ x - 3 ∣

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln ∣ x ∣ = ln (∣ x ∣^{2})

= ln (∣ x ∣^{2}) - ln ∣ x - 3 ∣

Apply log rule:

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

ln (∣ x ∣^{2}) - ln ∣ x - 3 ∣ = ln (\frac{∣ x ∣ ^{2}}{∣ x - 3 ∣})

= ln (\frac{∣ x ∣ ^{2}}{∣ x - 3 ∣})

∣ x ∣^{2} = x^{2}

= ln (\frac{x ^{2}}{∣ x - 3 ∣})

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Frequently Asked Questions (FAQ)

What is 2ln|x|-ln|x-3| ?
The solution to 2ln|x|-ln|x-3| is ln((x^2)/(|x-3|))