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Popular >

simplify ln(e^{2x}(1+x^3))

Solution

simplify

ln (e^{2 x} (1 + x^{3}))

Solution

2 x + ln (1 + x^{3})

Solution steps

ln (e^{2 x} (1 + x^{3}))

Apply log rule:

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

ln (e^{2 x} (1 + x^{3})) = ln (e^{2 x}) + ln (1 + x^{3})

= ln (e^{2 x}) + ln (x^{3} + 1)

Apply log rule:

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

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

= 2 x ln (e) + ln (1 + x^{3})

2 x ln (e) = 2 x

= 2 x + ln (x^{3} + 1)

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Frequently Asked Questions (FAQ)

What is ln(e^{2x}(1+x^3)) ?
The solution to ln(e^{2x}(1+x^3)) is 2x+ln(1+x^3)