What is simplify-log_{10}(2.7\times 10^{-2}) ?

The solution to simplify-log_{10}(2.7\times 10^{-2}) is -log_{10}(2.7)+2

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simplify-log_{10}(2.7\times 10^{-2})

simplify

- lo g_{10} (2.7 \cdot 1 0^{- 2})

- lo g_{10} (2.7) + 2

Decimal Notation

1.56863 \dots

Solution steps

- lo g_{10} (2.7 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (2.7 \cdot 1 0^{- 2}) = lo g_{10} (2.7) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (2.7) + 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} (2.7) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (2.7) - 2)

Distribute parentheses

= - (lo g_{10} (2.7)) - (- 2)

Apply minus-plus rules

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

= - lo g_{10} (2.7) + 2

lo g_{2} (x y^{2})

ln (\frac{e ^{6}}{5})

lo g_{10} (\frac{x}{y}) - lo g_{10} (\frac{y}{x})

ln (\frac{41}{10})

ln (\frac{x ^{5}}{5 ( 1 + x ) ^{4}})

What is simplify-log_{10}(2.7\times 10^{-2}) ?
The solution to simplify-log_{10}(2.7\times 10^{-2}) is -log_{10}(2.7)+2