What is log_{10}(3000)-log_{10}(15)-log_{10}(2) ?

The solution to log_{10}(3000)-log_{10}(15)-log_{10}(2) is 2

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simplify log_{10}(3000)-log_{10}(15)-log_{10}(2)

simplify

lo g_{10} (3000) - lo g_{10} (15) - lo g_{10} (2)

2

Solution steps

lo g_{10} (3000) - lo g_{10} (15) - lo g_{10} (2)

Apply log rule:

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

lo g_{10} (3000) - lo g_{10} (15) = lo g_{10} (\frac{3000}{15})

= lo g_{10} (\frac{3000}{15}) - lo g_{10} (2)

Apply log rule:

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

lo g_{10} (\frac{3000}{15}) - lo g_{10} (2) = lo g_{10} (\frac{\frac{3000}{15}}{2})

= lo g_{10} (\frac{\frac{3000}{15}}{2})

\frac{\frac{3000}{15}}{2} = 1 0^{2}

= lo g_{10} (1 0^{2})

Apply log rule:

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

= 2

\frac{\frac{16}{3}}{4}

- 10 \times 10

- 10 \times (- 1)

lo g_{5} (81)

i^{231}

What is log_{10}(3000)-log_{10}(15)-log_{10}(2) ?
The solution to log_{10}(3000)-log_{10}(15)-log_{10}(2) is 2