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Popular >

simplify ln(5*e^2)-ln(e)

Solution

simplify

ln (5 \cdot e^{2}) - ln (e)

Solution

ln (5) + 1

+1

Decimal Notation

2.60943 \dots

Solution steps

ln (5 e^{2}) - ln (e)

Apply log rule:

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

ln (5 e^{2}) = ln (5) + ln (e^{2})

= ln (5) + ln (e^{2}) - ln (e)

Apply log rule:

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

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

= ln (5) + 2 ln (e) - ln (e)

Add similar elements:

2 ln (e) - ln (e) = ln (e)

= ln (5) + ln (e)

Apply log rule:

lo g_{a} (a) = 1

= ln (5) + 1

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Frequently Asked Questions (FAQ)

What is ln(5*e^2)-ln(e) ?
The solution to ln(5*e^2)-ln(e) is ln(5)+1