What is 2ln|x|+2ln|x-3| ?

The solution to 2ln|x|+2ln|x-3| is ln(x^2(x-3)^2)

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

simplify

2 ln ∣ x ∣ + 2 ln ∣ x - 3 ∣

ln (x^{2} (x - 3)^{2})

Solution steps

2 ln ∣ x ∣ + 2 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}) + 2 ln ∣ x - 3 ∣

Apply log rule:

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

2 ln ∣ x - 3 ∣ = ln (∣ x - 3 ∣^{2})

= ln (∣ x ∣^{2}) + ln (∣ x - 3 ∣^{2})

Apply log rule:

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

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

= ln (∣ x ∣^{2} ∣ x - 3 ∣^{2})

Simplify

∣ x ∣^{2} ∣ x - 3 ∣^{2} : x^{2} (x - 3)^{2}

= ln (x^{2} (x - 3)^{2})

3 ln (\frac{x}{y})

3 ln (2) - ln (3)

14.77 + 10 \cdot lo g_{10} (\frac{179.68}{1.905})

- lo g_{10} (7.2 \cdot 1 0^{- 6})

4.3279 + lo g_{10} (\frac{0.47}{0.29})