What is 2log_{2}(7)+log_{2}(3) ?

The solution to 2log_{2}(7)+log_{2}(3) is log_{2}(147)

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simplify 2log_{2}(7)+log_{2}(3)

simplify

2 lo g_{2} (7) + lo g_{2} (3)

lo g_{2} (147)

Decimal Notation

7.19967 \dots

Solution steps

2 lo g_{2} (7) + lo g_{2} (3)

Apply log rule:

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

2 lo g_{2} (7) = lo g_{2} (7^{2})

= lo g_{2} (7^{2}) + lo g_{2} (3)

Apply log rule:

lo g_{a} (x) + lo g_{a} (y) = lo g_{a} (x y)

lo g_{2} (7^{2}) + lo g_{2} (3) = lo g_{2} (7^{2} \cdot 3)

= lo g_{2} (7^{2} \cdot 3)

7^{2} \cdot 3 = 147

= lo g_{2} (147)

ln (\frac{1}{8}) - ln (\frac{1}{2})

ln (\frac{x}{7})

ln (\frac{0.4}{0.6})

ln (\frac{18038.519}{72327.395})

lo g_{3} (9 a)

What is 2log_{2}(7)+log_{2}(3) ?
The solution to 2log_{2}(7)+log_{2}(3) is log_{2}(147)