What is 3/2 ln|4+3|+1/2 ln|x-3| ?

The solution to 3/2 ln|4+3|+1/2 ln|x-3| is ln(7sqrt(7)|x-3|^{1/2})

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simplify 3/2 ln|4+3|+1/2 ln|x-3|

simplify

\frac{3}{2} ln ∣ 4 + 3 ∣ + \frac{1}{2} ln ∣ x - 3 ∣

ln (77 ∣ x - 3 ∣^{\frac{1}{2}})

Solution steps

\frac{3}{2} ln ∣ 4 + 3 ∣ + \frac{1}{2} ln ∣ x - 3 ∣

Apply log rule:

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

\frac{3}{2} ln ∣ 4 + 3 ∣ = ln (∣ 4 + 3 ∣^{\frac{3}{2}})

= ln (∣ 4 + 3 ∣^{\frac{3}{2}}) + \frac{1}{2} ln ∣ x - 3 ∣

Apply log rule:

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

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

= ln (∣ 4 + 3 ∣^{\frac{3}{2}}) + ln (∣ x - 3 ∣^{\frac{1}{2}})

Apply log rule:

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

ln (∣ 4 + 3 ∣^{\frac{3}{2}}) + ln (∣ x - 3 ∣^{\frac{1}{2}}) = ln (∣ 4 + 3 ∣^{\frac{3}{2}} ∣ x - 3 ∣^{\frac{1}{2}})

= ln (∣ 4 + 3 ∣^{\frac{3}{2}} ∣ x - 3 ∣^{\frac{1}{2}})

∣ 4 + 3 ∣^{\frac{3}{2}} = 77

= ln (77 ∣ x - 3 ∣^{\frac{1}{2}})

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What is 3/2 ln|4+3|+1/2 ln|x-3| ?
The solution to 3/2 ln|4+3|+1/2 ln|x-3| is ln(7sqrt(7)|x-3|^{1/2})