What is 8ln(x^2e^x) ?

The solution to 8ln(x^2e^x) is 16ln(x)+8x

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simplify 8ln(x^2e^x)

simplify

8 ln (x^{2} e^{x})

16 ln (x) + 8 x

Solution steps

8 ln (x^{2} e^{x})

Apply log rule:

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

8 ln (x^{2} e^{x}) = 8 ln (x^{2}) + 8 ln (e^{x})

= 8 ln (x^{2}) + 8 ln (e^{x})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 8 \cdot 2 ln (x) + 8 ln (e^{x})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

= 8 \cdot 2 ln (x) + 8 x ln (e)

8 \cdot 2 ln (x) = 16 ln (x)

8 x ln (e) = 8 x

= 16 ln (x) + 8 x

\frac{2 ln ( 4 )}{ln ( 12 ) - ln ( 4 )}

- ln (c) + ln (c + x)

ln (87) - ln (22)

- lo g_{10} (8.4 \cdot 1 0^{- 6})

\frac{ln ( 10 ) - ln ( 8 )}{( 8 - 6 )}