What is simplify-log_{10}(6.3*10^{-2}) ?

The solution to simplify-log_{10}(6.3*10^{-2}) is -log_{10}(6.3)+2

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simplify-log_{10}(6.3*10^{-2})

simplify

- lo g_{10} (6.3 \cdot 1 0^{- 2})

- lo g_{10} (6.3) + 2

Decimal Notation

1.20065 \dots

Solution steps

- lo g_{10} (6.3 \cdot 1 0^{- 2})

Apply log rule:

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

lo g_{10} (6.3 \cdot 1 0^{- 2}) = lo g_{10} (6.3) + lo g_{10} (1 0^{- 2})

= - (lo g_{10} (6.3) + 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} (6.3) - 2 lo g_{10} (10))

2 lo g_{10} (10) = 2

= - (lo g_{10} (6.3) - 2)

Distribute parentheses

= - (lo g_{10} (6.3)) - (- 2)

Apply minus-plus rules

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

= - lo g_{10} (6.3) + 2

ln (x) - ln (x + 2)

ln ((2 x + 1)^{5} (x^{4} - 3)^{6})

ln (\frac{937.8}{30.84})

- lo g_{10} (8.65 \cdot 1 0^{- 9})

ln (a (2 + 3))

What is simplify-log_{10}(6.3*10^{-2}) ?
The solution to simplify-log_{10}(6.3*10^{-2}) is -log_{10}(6.3)+2