What is log_{2}(5)+log_{2}(12)-log_{2}(3.75) ?

The solution to log_{2}(5)+log_{2}(12)-log_{2}(3.75) is 4

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simplify log_{2}(5)+log_{2}(12)-log_{2}(3.75)

simplify

lo g_{2} (5) + lo g_{2} (12) - lo g_{2} (3.75)

4

Solution steps

lo g_{2} (5) + lo g_{2} (12) - lo g_{2} (3.75)

Apply log rule:

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

lo g_{2} (5) + lo g_{2} (12) = lo g_{2} (5 \cdot 12)

= lo g_{2} (5 \cdot 12) - lo g_{2} (3.75)

Multiply the numbers:

5 \cdot 12 = 60

= lo g_{2} (60) - lo g_{2} (3.75)

Apply log rule:

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

lo g_{2} (60) - lo g_{2} (3.75) = lo g_{2} (\frac{60}{3.75})

= lo g_{2} (\frac{60}{3.75})

Divide the numbers:

\frac{60}{3.75} = 16

= lo g_{2} (16)

Rewrite

16

in power-base form:

16 = 2^{4}

= lo g_{2} (2^{4})

Apply log rule:

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

lo g_{2} (2^{4}) = 4 lo g_{2} (2)

= 4 lo g_{2} (2)

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= 4 \cdot 1

Multiply the numbers:

4 \cdot 1 = 4

= 4

ln (x^{4} e^{2 x})

lo g_{10} (w) + lo g_{10} (v) - 3 lo g_{10} (z)

ln (\frac{205}{200}) + (\frac{1}{2} \cdot 0.0 2^{2} - 0.05) \cdot 0.25

4 ln (y) - \frac{1}{5} ln (x) + 9 ln (z)

ln (\frac{4}{7 - x})

What is log_{2}(5)+log_{2}(12)-log_{2}(3.75) ?
The solution to log_{2}(5)+log_{2}(12)-log_{2}(3.75) is 4