What is log_{10}((2.51*10^{-9})/x) ?

The solution to log_{10}((2.51*10^{-9})/x) is log_{10}(251)-11-log_{10}(x)

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simplify log_{10}((2.51*10^{-9})/x)

simplify

lo g_{10} (\frac{2.51 \cdot 1 0 ^{- 9}}{x})

lo g_{10} (251) - 11 - lo g_{10} (x)

Solution steps

lo g_{10} (\frac{2.51 \cdot 1 0 ^{- 9}}{x})

Simplify

\frac{2.51 \cdot 1 0 ^{- 9}}{x} : \frac{251}{100000000000 x}

= lo g_{10} (\frac{251}{100000000000 x})

Apply log rule:

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

lo g_{10} (\frac{251}{100000000000 x}) = lo g_{10} (251) - lo g_{10} (100000000000 x)

= lo g_{10} (251) - lo g_{10} (100000000000 x)

Simplify

lo g_{10} (100000000000 x) : 11 + lo g_{10} (x)

= lo g_{10} (251) - (11 + lo g_{10} (x))

Apply the distributive law:

- (a + b) = - a - b

- (11 + lo g_{10} (x)) = - 11 - lo g_{10} (x)

= lo g_{10} (251) - 11 - lo g_{10} (x)

- lo g_{10} (4.34 \cdot 1 0^{- 6})

2 lo g_{10} (y^{3}) + lo g_{10} (y^{2})

lo g_{a} (x^{2}) - 2 lo g_{a} (x)

4 lo g_{3} (x^{2} - 1) - 2 lo g_{3} (x + 1)

lo g_{3} (7 \cdot 5)

What is log_{10}((2.51*10^{-9})/x) ?
The solution to log_{10}((2.51*10^{-9})/x) is log_{10}(251)-11-log_{10}(x)