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Popular >

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

Solution

simplify

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

Solution

ln (2) + 2 x + 1 + ln (x)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= ln (2) + (2 x + 1) ln (e) + ln (x)

(2 x + 1) ln (e) = 2 x + 1

= ln (2) + 2 x + 1 + ln (x)

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Frequently Asked Questions (FAQ)

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