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Popular >

simplify log_{10}(20x)

Solution

simplify

lo g_{10} (20 x)

Solution

1 + lo g_{10} (2) + lo g_{10} (x)

Solution steps

lo g_{10} (20 x)

Factor the number:

20 = 10 \cdot 2

= lo g_{10} (10 \cdot 2 x)

Apply log rule:

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

lo g_{10} (10 \cdot 2 x) = lo g_{10} (10) + lo g_{10} (2 x)

= lo g_{10} (10) + lo g_{10} (2 x)

Apply log rule:

lo g_{a} (a) = 1

lo g_{10} (10) = 1

= 1 + lo g_{10} (2 x)

Apply log rule:

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

lo g_{10} (2 x) = lo g_{10} (2) + lo g_{10} (x)

= 1 + (lo g_{10} (2) + lo g_{10} (x))

Apply rule:

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

1 + (lo g_{10} (2) + lo g_{10} (x)) = 1 + lo g_{10} (2) + lo g_{10} (x)

= 1 + lo g_{10} (2) + lo g_{10} (x)

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Frequently Asked Questions (FAQ)

What is log_{10}(20x) ?
The solution to log_{10}(20x) is 1+log_{10}(2)+log_{10}(x)