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Popular >

simplify ln(e^xx^3(x+1)^4)

Solution

simplify

ln (e^{x} x^{3} (x + 1)^{4})

Solution

x + 3 ln (x) + 4 ln (x + 1)

Solution steps

ln (e^{x} x^{3} (x + 1)^{4})

Apply log rule:

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

ln (e^{x} x^{3} (x + 1)^{4}) = ln (e^{x}) + ln (x^{3}) + ln ((x + 1)^{4})

= ln (e^{x}) + ln (x^{3}) + ln ((x + 1)^{4})

Apply log rule:

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

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

= x ln (e) + ln (x^{3}) + ln ((x + 1)^{4})

Apply log rule:

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

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

= x ln (e) + 3 ln (x) + ln ((x + 1)^{4})

Apply log rule:

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

ln ((x + 1)^{4}) = 4 ln (x + 1)

= x ln (e) + 3 ln (x) + 4 ln (x + 1)

x ln (e) = x

= x + 3 ln (x) + 4 ln (x + 1)

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Frequently Asked Questions (FAQ)

What is ln(e^xx^3(x+1)^4) ?
The solution to ln(e^xx^3(x+1)^4) is x+3ln(x)+4ln(x+1)