What is 2log_{2}(3)+log_{2}(5) ?

The solution to 2log_{2}(3)+log_{2}(5) is log_{2}(45)

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simplify 2log_{2}(3)+log_{2}(5)

simplify

2 lo g_{2} (3) + lo g_{2} (5)

lo g_{2} (45)

Decimal Notation

5.49185 \dots

Solution steps

2 lo g_{2} (3) + lo g_{2} (5)

Apply log rule:

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

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

= lo g_{2} (3^{2}) + lo g_{2} (5)

Apply log rule:

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

lo g_{2} (3^{2}) + lo g_{2} (5) = lo g_{2} (3^{2} \cdot 5)

= lo g_{2} (3^{2} \cdot 5)

3^{2} \cdot 5 = 45

= lo g_{2} (45)

ln (\frac{1}{9 k})

3 (2 \cdot lo g_{10} (a) - lo g_{10} (b))

lo g_{8} (\frac{x y ^{5}}{z ^{6}})

6 ln (x) - \frac{1}{8} ln (y)

What is 2log_{2}(3)+log_{2}(5) ?
The solution to 2log_{2}(3)+log_{2}(5) is log_{2}(45)