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)

- 2.55 lo g_{10} (\frac{B}{B o})

\frac{( 0.35 ) ^{2} \cdot 13.86}{100 \cdot 61} \cdot ln (\frac{113}{100})

8 lo g_{b} (x) + 2 lo g_{b} (z)

- \frac{2 ln ( 10 x + 5 y - 2 )}{25} + \frac{2 x + y}{5}

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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)