What is simplify-log_{10}(1.83*10^{-6}) ?

The solution to simplify-log_{10}(1.83*10^{-6}) is -log_{10}(1.83)+6

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simplify-log_{10}(1.83*10^{-6})

simplify

- lo g_{10} (1.83 \cdot 1 0^{- 6})

- lo g_{10} (1.83) + 6

Decimal Notation

5.73754 \dots

Solution steps

- lo g_{10} (1.83 \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (1.83 \cdot 1 0^{- 6}) = lo g_{10} (1.83) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (1.83) + lo g_{10} (1 0^{- 6}))

Apply log rule:

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

lo g_{10} (1 0^{- 6}) = - 6 lo g_{10} (10)

= - (lo g_{10} (1.83) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (1.83) - 6)

Distribute parentheses

= - (lo g_{10} (1.83)) - (- 6)

Apply minus-plus rules

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

= - lo g_{10} (1.83) + 6

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What is simplify-log_{10}(1.83*10^{-6}) ?
The solution to simplify-log_{10}(1.83*10^{-6}) is -log_{10}(1.83)+6