What is simplify-log_{10}(2.5x10^{-4}) ?

The solution to simplify-log_{10}(2.5x10^{-4}) is -log_{10}(2.5)-log_{10}(x)+4

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simplify-log_{10}(2.5x10^{-4})

simplify

- lo g_{10} (2.5 x 1 0^{- 4})

- lo g_{10} (2.5) - lo g_{10} (x) + 4

Solution steps

- lo g_{10} (2.5 x \cdot 1 0^{- 4})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{10} (2.5 x \cdot 1 0^{- 4}) = lo g_{10} (2.5) + lo g_{10} (x) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (x) + lo g_{10} (2.5) + lo g_{10} (1 0^{- 4}))

Apply log rule:

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

lo g_{10} (1 0^{- 4}) = - 4 lo g_{10} (10)

= - (lo g_{10} (2.5) + lo g_{10} (x) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (x) + lo g_{10} (2.5) - 4)

Distribute parentheses

= - (lo g_{10} (2.5)) - (lo g_{10} (x)) - (- 4)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - lo g_{10} (2.5) - lo g_{10} (x) + 4

ln (\frac{- 2}{3} e^{3 x})

ln (- \frac{1}{5} e^{- 5 x})

ln (a (x - 3)^{- 1})

ln (x^{3} e^{2 x - 1})

lo g_{10} (\frac{150}{3.6}) + 1.9

What is simplify-log_{10}(2.5x10^{-4}) ?
The solution to simplify-log_{10}(2.5x10^{-4}) is -log_{10}(2.5)-log_{10}(x)+4