What is (8(ln|x+3|-ln|x+4|))/x ?

The solution to (8(ln|x+3|-ln|x+4|))/x is (8ln((|x+3|)/(|x+4|)))/x

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simplify (8(ln|x+3|-ln|x+4|))/x

simplify

\frac{8 ( ln ∣ x + 3 ∣ - ln ∣ x + 4 ∣ )}{x}

\frac{8 ln ( \frac{∣ x + 3 ∣}{∣ x + 4 ∣} )}{x}

Solution steps

\frac{8 ( ln ∣ x + 3 ∣ - ln ∣ x + 4 ∣ )}{x}

Apply log rule:

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

ln ∣ x + 3 ∣ - ln ∣ x + 4 ∣ = ln (\frac{∣ x + 3 ∣}{∣ x + 4 ∣})

= \frac{8 ln ( \frac{∣ x + 3 ∣}{∣ x + 4 ∣} )}{x}

lo g_{10} (x + 2) - 2 lo g_{10} (x)

ln (150 e^{- x})

- 4 ln (\frac{3}{4})

3 lo g_{5} (u) - 3 lo g_{5} (v)

lo g_{10} (\frac{\frac{1}{( 1 + c o t ^{2} ( x ) ) ^{1}}}{2})

What is (8(ln|x+3|-ln|x+4|))/x ?
The solution to (8(ln|x+3|-ln|x+4|))/x is (8ln((|x+3|)/(|x+4|)))/x