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Popular >

simplify 2ln(2)-ln|4+x^2|

Solution

simplify

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

Solution

ln (\frac{4}{∣ 4 + x ^{2} ∣})

Solution steps

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

Apply log rule:

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

2 ln (2) = ln (2^{2})

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

Apply log rule:

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

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

= ln (\frac{2 ^{2}}{∣ 4 + x ^{2} ∣})

2^{2} = 4

= ln (\frac{4}{∣ 4 + x ^{2} ∣})

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Frequently Asked Questions (FAQ)

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