What is log_{10}(15/4)+log_{10}(400000/15) ?

The solution to log_{10}(15/4)+log_{10}(400000/15) is 5

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simplify log_{10}(15/4)+log_{10}(400000/15)

simplify

lo g_{10} (\frac{15}{4}) + lo g_{10} (\frac{400000}{15})

5

Solution steps

lo g_{10} (\frac{15}{4}) + lo g_{10} (\frac{400000}{15})

Apply log rule:

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

lo g_{10} (\frac{15}{4}) + lo g_{10} (\frac{400000}{15}) = lo g_{10} (\frac{15}{4} \cdot \frac{400000}{15})

= lo g_{10} (\frac{15}{4} \cdot \frac{400000}{15})

\frac{15}{4} \cdot \frac{400000}{15} = 100000

= lo g_{10} (100000)

Factor the number:

100000 = 1 0^{5}

= lo g_{10} (1 0^{5})

Apply log rule:

lo g_{a} (a^{b}) = b

= 5

lo g_{9} (\frac{x}{w})

lo g_{7} (\frac{1}{7} m n^{2})

- ln ∣ v + 1 ∣ - \frac{1}{2} - ln v^{2} 11

lo g_{9} (\frac{x}{y})

4 (\frac{1}{9} ln ∣ x - 2 ∣ - \frac{1}{9} ln ∣ x + 7 ∣ + C)

What is log_{10}(15/4)+log_{10}(400000/15) ?
The solution to log_{10}(15/4)+log_{10}(400000/15) is 5