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Popular >

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

Solution

simplify

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

Solution

2 ln (x) + 2 x

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 ln (x) + 2 x ln (e)

2 x ln (e) = 2 x

= 2 ln (x) + 2 x

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Frequently Asked Questions (FAQ)

What is ln(x^2e^{2x}) ?
The solution to ln(x^2e^{2x}) is 2ln(x)+2x