What is simplify-log_{10}(3.3*10^{-1}) ?

The solution to simplify-log_{10}(3.3*10^{-1}) is -log_{10}(3.3)+1

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simplify-log_{10}(3.3*10^{-1})

simplify

- lo g_{10} (3.3 \cdot 1 0^{- 1})

- lo g_{10} (3.3) + 1

Decimal Notation

0.48148 \dots

Solution steps

- lo g_{10} (3.3 \cdot 1 0^{- 1})

Apply log rule:

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

lo g_{10} (3.3 \cdot 1 0^{- 1}) = lo g_{10} (3.3) + lo g_{10} (1 0^{- 1})

= - (lo g_{10} (3.3) + 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} (3.3) - 1 \cdot lo g_{10} (10))

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

= - (lo g_{10} (3.3) - 1)

Distribute parentheses

= - (lo g_{10} (3.3)) - (- 1)

Apply minus-plus rules

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

= - lo g_{10} (3.3) + 1

\frac{\partial}{\partial x} (x y) + 2 x - ln (x^{2} y)

ln (\frac{( 4 x ^{2} + 5 ) ^{3}}{( 3 x - 7 ) ^{2} ( 5 x ^{2} - 3 x ) ^{4}})

2 ln (3) + 2 ln (2)

\frac{3}{2} \cdot ln^{3} (3)

- lo g_{10} (1.58 \cdot 1 0^{- 3})

What is simplify-log_{10}(3.3*10^{-1}) ?
The solution to simplify-log_{10}(3.3*10^{-1}) is -log_{10}(3.3)+1