What is simplify-log_{10}(1.6x10^{-4}) ?

The solution to simplify-log_{10}(1.6x10^{-4}) is -log_{10}(1.6)-log_{10}(x)+4

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simplify-log_{10}(1.6x10^{-4})

simplify

- lo g_{10} (1.6 x 1 0^{- 4})

- lo g_{10} (1.6) - lo g_{10} (x) + 4

Solution steps

- lo g_{10} (1.6 x \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (1.6 x \cdot 1 0^{- 4}) = lo g_{10} (1.6) + lo g_{10} (x) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (x) + lo g_{10} (1.6) + 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} (1.6) + lo g_{10} (x) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (x) + lo g_{10} (1.6) - 4)

Distribute parentheses

= - (lo g_{10} (1.6)) - (lo g_{10} (x)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (1.6) - lo g_{10} (x) + 4

ln (y^{2} + 5) - ln (y^{2} - 2)

lo g_{6} (\frac{1}{120})

x + ln (x) + ln (2)

\frac{ln ( x ) - ln ( 3 )}{x - 3}

27.7 ln (\frac{142}{x})

What is simplify-log_{10}(1.6x10^{-4}) ?
The solution to simplify-log_{10}(1.6x10^{-4}) is -log_{10}(1.6)-log_{10}(x)+4