What is log_{2}(10x) ?

The solution to log_{2}(10x) is 1+log_{2}(5)+log_{2}(x)

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simplify log_{2}(10x)

simplify

lo g_{2} (10 x)

1 + lo g_{2} (5) + lo g_{2} (x)

Solution steps

lo g_{2} (10 x)

Factor the number:

10 = 2 \cdot 5

= lo g_{2} (2 \cdot 5 x)

Apply log rule:

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

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

= lo g_{2} (2) + lo g_{2} (5 x)

Apply log rule:

lo g_{a} (a) = 1

lo g_{2} (2) = 1

= 1 + lo g_{2} (5 x)

Apply log rule:

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

lo g_{2} (5 x) = lo g_{2} (5) + lo g_{2} (x)

= 1 + (lo g_{2} (5) + lo g_{2} (x))

Apply rule:

a + (b + c) = a + b + c

1 + (lo g_{2} (5) + lo g_{2} (x)) = 1 + lo g_{2} (5) + lo g_{2} (x)

= 1 + lo g_{2} (5) + lo g_{2} (x)

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