What is ln(1/2 e^{2.3}) ?

The solution to ln(1/2 e^{2.3}) is -ln(2)+2.3

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simplify ln(1/2 e^{2.3})

simplify

ln (\frac{1}{2} e^{2.3})

- ln (2) + 2.3

Decimal Notation

1.60685 \dots

Solution steps

ln (\frac{1}{2} e^{2.3})

Apply log rule:

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

ln (\frac{1}{2} e^{2.3}) = ln (\frac{1}{2}) + ln (e^{2.3})

= ln (\frac{1}{2}) + ln (e^{2.3})

Apply log rule:

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

ln (e^{2.3}) = 2.3 ln (e)

= ln (\frac{1}{2}) + 2.3 ln (e)

Apply log rule:

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

ln (\frac{1}{2}) = ln (1) - ln (2)

= ln (1) - ln (2) + 2.3 ln (e)

ln (1) = 0

2.3 ln (e) = 2.3

= 0 - ln (2) + 2.3

Add the numbers:

0 + 2.3 = 2.3

= - ln (2) + 2.3

- \frac{2 ln ( 2 )}{3}

ln (\frac{( e - e ^{- 1} )}{2})

4 ln (a) + 8 ln (b)

ln (\frac{x}{298}) \cdot 4.87

ln (A B e^{- 4})