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Popular >

simplify ln(e^2)+ln(2e)

Solution

simplify

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

Solution

3 + ln (2)

+1

Decimal Notation

3.69314 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Group like terms

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

Add similar elements:

2 ln (e) + ln (e) = 3 ln (e)

= 3 ln (e) + ln (2)

3 ln (e) = 3

= 3 + ln (2)

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Frequently Asked Questions (FAQ)

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