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Popular >

simplify ln(4x^3e^x)

Solution

simplify

ln (4 x^{3} e^{x})

Solution

2 ln (2) + 3 ln (x) + x

Solution steps

ln (4 x^{3} e^{x})

Apply log rule:

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

ln (4 x^{3} e^{x}) = ln (4) + ln (x^{3}) + ln (e^{x})

= ln (4) + ln (x^{3}) + ln (e^{x})

Apply log rule:

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

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

= ln (4) + 3 ln (x) + ln (e^{x})

Apply log rule:

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

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

= ln (4) + 3 ln (x) + x ln (e)

x ln (e) = x

= ln (4) + 3 ln (x) + x

ln (4) = 2 ln (2)

= 2 ln (2) + 3 ln (x) + x

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Frequently Asked Questions (FAQ)

What is ln(4x^3e^x) ?
The solution to ln(4x^3e^x) is 2ln(2)+3ln(x)+x