What is log_{2}(7/11 e^{15/4})-10 ?

The solution to log_{2}(7/11 e^{15/4})-10 is log_{2}(7)-log_{2}(11)+15/4 log_{2}(e)-10

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simplify log_{2}(7/11 e^{15/4})-10

simplify

lo g_{2} (\frac{7}{11} e^{\frac{15}{4}}) - 10

lo g_{2} (7) - lo g_{2} (11) + \frac{15}{4} lo g_{2} (e) - 10

Decimal Notation

- 5.24197 \dots

Solution steps

lo g_{2} (\frac{7}{11} e^{\frac{15}{4}}) - 10

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}}) - 10

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) - 10

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) - 10

ln (x) - 4 ln (4)

lo g_{10} (12 + \frac{1}{2}) lo g_{10} (7) - lo g_{10} (2)

110 (ln (24) - ln (19)) + 55

5 ln (\cdot 5 l^{2})

2 lo g_{10} (\frac{5}{4})

What is log_{2}(7/11 e^{15/4})-10 ?
The solution to log_{2}(7/11 e^{15/4})-10 is log_{2}(7)-log_{2}(11)+15/4 log_{2}(e)-10