What is ln(10)+3ln(x)+2ln(x^2+10) ?

The solution to ln(10)+3ln(x)+2ln(x^2+10) is ln(10x^3(x^2+10)^2)

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simplify ln(10)+3ln(x)+2ln(x^2+10)

simplify

ln (10) + 3 ln (x) + 2 ln (x^{2} + 10)

ln (10 x^{3} (x^{2} + 10)^{2})

Solution steps

ln (10) + 3 ln (x) + 2 ln (x^{2} + 10)

Apply log rule:

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

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

= ln (10) + ln (x^{3}) + 2 ln (x^{2} + 10)

Apply log rule:

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

ln (10) + ln (x^{3}) = ln (10 x^{3})

= ln (10 x^{3}) + 2 ln (x^{2} + 10)

Apply log rule:

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

2 ln (x^{2} + 10) = ln ((x^{2} + 10)^{2})

= ln (10 x^{3}) + ln ((x^{2} + 10)^{2})

Apply log rule:

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

ln (10 x^{3}) + ln ((x^{2} + 10)^{2}) = ln (10 x^{3} (x^{2} + 10)^{2})

= ln (10 x^{3} (x^{2} + 10)^{2})

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ln (e e \frac{1}{2})

What is ln(10)+3ln(x)+2ln(x^2+10) ?
The solution to ln(10)+3ln(x)+2ln(x^2+10) is ln(10x^3(x^2+10)^2)