What is simplify-1/4 ln|x+3|+1/4 ln|x+7| ?

The solution to simplify-1/4 ln|x+3|+1/4 ln|x+7| is ln(\sqrt[4]{(|x+7|)/(|x+3|)})

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simplify-1/4 ln|x+3|+1/4 ln|x+7|

simplify

- \frac{1}{4} ln ∣ x + 3 ∣ + \frac{1}{4} ln ∣ x + 7 ∣

Solution steps

- \frac{1}{4} ln ∣ x + 3 ∣ + \frac{1}{4} ln ∣ x + 7 ∣

Apply log rule:

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

\frac{1}{4} ln ∣ x + 3 ∣ = ln (∣ x + 3 ∣^{\frac{1}{4}})

= - ln (∣ x + 3 ∣^{\frac{1}{4}}) + \frac{1}{4} ln ∣ x + 7 ∣

Apply log rule:

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

\frac{1}{4} ln ∣ x + 7 ∣ = ln (∣ x + 7 ∣^{\frac{1}{4}})

= - ln (∣ x + 3 ∣^{\frac{1}{4}}) + ln (∣ x + 7 ∣^{\frac{1}{4}})

Apply log rule:

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

ln (∣ x + 7 ∣^{\frac{1}{4}}) - ln (∣ x + 3 ∣^{\frac{1}{4}}) = ln (\frac{∣ x + 7 ∣ ^{\frac{1}{4}}}{∣ x + 3 ∣ ^{\frac{1}{4}}})

= ln (\frac{∣ x + 7 ∣ ^{\frac{1}{4}}}{∣ x + 3 ∣ ^{\frac{1}{4}}})

Combine same powers :

x \frac{\partial}{\partial x} (y) + ln (x y) + x

ln (\frac{95 \cdot 1 0 ^{12} ( 2.5 )}{1 0 ^{- 3}})

ln (2) - \frac{1}{2} ln (3)

(\frac{1}{2}) (3 ln (x + 3) + ln (x) - ln (x^{2} - 1))

ln (\frac{1643.85}{547.85}) \cdot 10

What is simplify-1/4 ln|x+3|+1/4 ln|x+7| ?
The solution to simplify-1/4 ln|x+3|+1/4 ln|x+7| is ln(\sqrt[4]{(|x+7|)/(|x+3|)})