What is 3ln|x-2|+4ln|x+7| ?

The solution to 3ln|x-2|+4ln|x+7| is ln(|x-2|^3(x+7)^4)

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simplify 3ln|x-2|+4ln|x+7|

simplify

3 ln ∣ x - 2 ∣ + 4 ln ∣ x + 7 ∣

ln (∣ x - 2 ∣^{3} (x + 7)^{4})

Solution steps

3 ln ∣ x - 2 ∣ + 4 ln ∣ x + 7 ∣

Apply log rule:

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

3 ln ∣ x - 2 ∣ = ln (∣ x - 2 ∣^{3})

= ln (∣ x - 2 ∣^{3}) + 4 ln ∣ x + 7 ∣

Apply log rule:

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

4 ln ∣ x + 7 ∣ = ln (∣ x + 7 ∣^{4})

= ln (∣ x - 2 ∣^{3}) + ln (∣ x + 7 ∣^{4})

Apply log rule:

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

ln (∣ x - 2 ∣^{3}) + ln (∣ x + 7 ∣^{4}) = ln (∣ x + 7 ∣^{4} ∣ x - 2 ∣^{3})

= ln (∣ x + 7 ∣^{4} ∣ x - 2 ∣^{3})

∣ x + 7 ∣^{4} = (x + 7)^{4}

= ln (∣ x - 2 ∣^{3} (x + 7)^{4})

4.3 + lo g_{10} (\frac{0.02}{0.05})

\frac{1}{2} ln (x) + 8 ln (x^{3}) - 3 ln (x - 2)

lo g_{10} (25) + lo g_{10} (2) + lo g_{10} (0.02)

ln (\frac{0.017}{1})

ln (2 e^{2 t})

What is 3ln|x-2|+4ln|x+7| ?
The solution to 3ln|x-2|+4ln|x+7| is ln(|x-2|^3(x+7)^4)