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Popular >

simplify ln(8/(e^{ln(2))})

Solution

simplify

ln (\frac{8}{e ^{l n (2)}})

Solution

2 ln (2)

+1

Decimal Notation

1.38629 \dots

Solution steps

ln (\frac{8}{e ^{l n (2)}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{8}{e ^{l n (2)}}) = ln (8) - ln (e^{l n (2)})

= ln (8) - ln (e^{l n (2)})

Apply log rule:

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

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

= ln (8) - ln (2) ln (e)

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

= ln (8) - ln (2)

ln (8) = 3 ln (2)

= 3 ln (2) - ln (2)

Add similar elements:

3 ln (2) - ln (2) = 2 ln (2)

= 2 ln (2)

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Frequently Asked Questions (FAQ)

What is ln(8/(e^{ln(2))}) ?
The solution to ln(8/(e^{ln(2))}) is 2ln(2)