What is simplify-log_{10}(2x10^{-4}) ?

The solution to simplify-log_{10}(2x10^{-4}) is -log_{10}(2)-log_{10}(x)+4

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simplify-log_{10}(2x10^{-4})

simplify

- lo g_{10} (2 x 1 0^{- 4})

- lo g_{10} (2) - lo g_{10} (x) + 4

Solution steps

- lo g_{10} (2 x \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (2 x \cdot 1 0^{- 4}) = lo g_{10} (2) + lo g_{10} (x) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (x) + lo g_{10} (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} (2) + lo g_{10} (x) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (x) + lo g_{10} (2) - 4)

Distribute parentheses

= - (lo g_{10} (2)) - (lo g_{10} (x)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (2) - lo g_{10} (x) + 4

ln (y) - 4 ln (x)

- ln (y) + ln (y - 1)

ln (3) + 4 ln (2) - ln (6)

ln (\frac{55}{60}) 7

ln ((4 x + 1)^{c o t (x)})

What is simplify-log_{10}(2x10^{-4}) ?
The solution to simplify-log_{10}(2x10^{-4}) is -log_{10}(2)-log_{10}(x)+4