What is log_{10}(20)-log_{10}(5) ?

The solution to log_{10}(20)-log_{10}(5) is 2log_{10}(2)

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simplify log_{10}(20)-log_{10}(5)

simplify

lo g_{10} (20) - lo g_{10} (5)

2 lo g_{10} (2)

Decimal Notation

0.60205 \dots

Solution steps

lo g_{10} (20) - lo g_{10} (5)

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{10} (20) - lo g_{10} (5) = lo g_{10} (\frac{20}{5})

= lo g_{10} (\frac{20}{5})

Divide the numbers:

\frac{20}{5} = 4

= lo g_{10} (4)

Factor the number:

4 = 2^{2}

= lo g_{10} (2^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), x > 0

lo g_{10} (2^{2}) = 2 lo g_{10} (2)

= 2 lo g_{10} (2)

lo g_{10} (10000 y)

lo g_{10} (x^{2}) - lo g_{10} (y) - lo g_{10} (x)

lo g_{10} (\frac{2}{ab})

lo g_{10} (\frac{z ^{5}}{y x ^{3}})

lo g_{7} (2401 x)

What is log_{10}(20)-log_{10}(5) ?
The solution to log_{10}(20)-log_{10}(5) is 2log_{10}(2)