What is simplify-log_{10}(4.2x10^{-4}) ?

The solution to simplify-log_{10}(4.2x10^{-4}) is -log_{10}(4.2)-log_{10}(x)+4

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simplify-log_{10}(4.2x10^{-4})

simplify

- lo g_{10} (4.2 x 1 0^{- 4})

- lo g_{10} (4.2) - lo g_{10} (x) + 4

Solution steps

- lo g_{10} (4.2 x \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (4.2 x \cdot 1 0^{- 4}) = lo g_{10} (4.2) + lo g_{10} (x) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (x) + lo g_{10} (4.2) + 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} (4.2) + lo g_{10} (x) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (x) + lo g_{10} (4.2) - 4)

Distribute parentheses

= - (lo g_{10} (4.2)) - (lo g_{10} (x)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (4.2) - lo g_{10} (x) + 4

ln (x) - 2 ln (x^{2} + 1) + \frac{1}{2} ln (x^{4} + 1)

3 lo g_{2} (\frac{5 x}{7})

- lo g_{10} (3.6 e^{- 13})

ln (7.83) - 6 ln (10)

What is simplify-log_{10}(4.2x10^{-4}) ?
The solution to simplify-log_{10}(4.2x10^{-4}) is -log_{10}(4.2)-log_{10}(x)+4