What is simplify-log_{10}(5*10^{-1}) ?

The solution to simplify-log_{10}(5*10^{-1}) is -log_{10}(5)+1

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simplify-log_{10}(5*10^{-1})

simplify

- lo g_{10} (5 \cdot 1 0^{- 1})

- lo g_{10} (5) + 1

Decimal Notation

0.30102 \dots

Solution steps

- lo g_{10} (5 \cdot 1 0^{- 1})

Apply log rule:

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

lo g_{10} (5 \cdot 1 0^{- 1}) = lo g_{10} (5) + lo g_{10} (1 0^{- 1})

= - (lo g_{10} (5) + lo g_{10} (1 0^{- 1}))

Apply log rule:

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

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

= - (lo g_{10} (5) - 1 \cdot lo g_{10} (10))

1 \cdot lo g_{10} (10) = 1

= - (lo g_{10} (5) - 1)

Distribute parentheses

= - (lo g_{10} (5)) - (- 1)

Apply minus-plus rules

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

= - lo g_{10} (5) + 1

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What is simplify-log_{10}(5*10^{-1}) ?
The solution to simplify-log_{10}(5*10^{-1}) is -log_{10}(5)+1