What is log_{2}(7/11 e^{(15/4)}) ?

The solution to log_{2}(7/11 e^{(15/4)}) is log_{2}(7)-log_{2}(11)+15/4 log_{2}(e)

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simplify log_{2}(7/11 e^{(15/4)})

simplify

lo g_{2} (\frac{7}{11} e^{(\frac{15}{4})})

lo g_{2} (7) - lo g_{2} (11) + \frac{15}{4} lo g_{2} (e)

Decimal Notation

4.75802 \dots

Solution steps

lo g_{2} (\frac{7}{11} e^{(\frac{15}{4})})

Apply log rule:

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

lo g_{2} (\frac{7}{11} e^{(\frac{15}{4})}) = lo g_{2} (\frac{7}{11}) + lo g_{2} (e^{(\frac{15}{4})})

= lo g_{2} (\frac{7}{11}) + lo g_{2} (e^{(\frac{15}{4})})

Apply log rule:

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

lo g_{2} (e^{(\frac{15}{4})}) = \frac{15}{4} lo g_{2} (e)

= lo g_{2} (\frac{7}{11}) + \frac{15}{4} lo g_{2} (e)

Apply log rule:

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

lo g_{2} (\frac{7}{11}) = lo g_{2} (7) - lo g_{2} (11)

= lo g_{2} (7) - lo g_{2} (11) + \frac{15}{4} lo g_{2} (e)

6 lo g_{5} (x) - 5 lo g_{5} (y)

ln (\frac{3 x - 5}{2 x - 1})

(\frac{1}{2} ln ∣ 2 (10) + 1 ∣ + 2 ln ∣ 10 - 1 ∣) - 5

ln (\frac{( 1 + 10 x )}{x})

ln (I) - ln (I - N)

What is log_{2}(7/11 e^{(15/4)}) ?
The solution to log_{2}(7/11 e^{(15/4)}) is log_{2}(7)-log_{2}(11)+15/4 log_{2}(e)