What is simplify-log_{10}(1.4*10^{-2}) ?

The solution to simplify-log_{10}(1.4*10^{-2}) is -log_{10}(1.4)+2

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simplify-log_{10}(1.4*10^{-2})

simplify

- lo g_{10} (1.4 \cdot 1 0^{- 2})

- lo g_{10} (1.4) + 2

Decimal Notation

1.85387 \dots

Solution steps

- lo g_{10} (1.4 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (1.4 \cdot 1 0^{- 2}) = lo g_{10} (1.4) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (1.4) + lo g_{10} (1 0^{- 2}))

Apply log rule:

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

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

= - (lo g_{10} (1.4) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (1.4) - 2)

Distribute parentheses

= - (lo g_{10} (1.4)) - (- 2)

Apply minus-plus rules

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

= - lo g_{10} (1.4) + 2

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What is simplify-log_{10}(1.4*10^{-2}) ?
The solution to simplify-log_{10}(1.4*10^{-2}) is -log_{10}(1.4)+2