What is simplify-log_{10}(2.5x*10^{-7}) ?

The solution to simplify-log_{10}(2.5x*10^{-7}) is -log_{10}(2.5)-log_{10}(x)+7

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simplify-log_{10}(2.5x*10^{-7})

simplify

- lo g_{10} (2.5 x \cdot 1 0^{- 7})

- lo g_{10} (2.5) - lo g_{10} (x) + 7

Solution steps

- lo g_{10} (2.5 x \cdot 1 0^{- 7})

Apply log rule:

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

lo g_{10} (2.5 x \cdot 1 0^{- 7}) = lo g_{10} (2.5) + lo g_{10} (x) + lo g_{10} (1 0^{- 7})

= - (lo g_{10} (x) + lo g_{10} (2.5) + lo g_{10} (1 0^{- 7}))

Apply log rule:

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

lo g_{10} (1 0^{- 7}) = - 7 lo g_{10} (10)

= - (lo g_{10} (2.5) + lo g_{10} (x) - 7 lo g_{10} (10))

7 lo g_{10} (10) = 7

= - (lo g_{10} (x) + lo g_{10} (2.5) - 7)

Distribute parentheses

= - (lo g_{10} (2.5)) - (lo g_{10} (x)) - (- 7)

Apply minus-plus rules

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

= - lo g_{10} (2.5) - lo g_{10} (x) + 7

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4 lo g_{8} (a) + lo g_{8} (77)

What is simplify-log_{10}(2.5x*10^{-7}) ?
The solution to simplify-log_{10}(2.5x*10^{-7}) is -log_{10}(2.5)-log_{10}(x)+7