What is simplify-log_{10}(424*10^{(-3)}) ?

The solution to simplify-log_{10}(424*10^{(-3)}) is -log_{10}(424)+3

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simplify-log_{10}(424*10^{(-3)})

simplify

- lo g_{10} (424 \cdot 1 0^{(- 3)})

- lo g_{10} (424) + 3

Decimal Notation

0.37263 \dots

Solution steps

- lo g_{10} (424 \cdot 1 0^{(- 3)})

Apply log rule:

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

lo g_{10} (424 \cdot 1 0^{(- 3)}) = lo g_{10} (424) + lo g_{10} (1 0^{(- 3)})

= - (lo g_{10} (424) + lo g_{10} (1 0^{(- 3)}))

Apply log rule:

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

lo g_{10} (1 0^{(- 3)}) = (- 3) lo g_{10} (10)

= - (lo g_{10} (424) + (- 3) lo g_{10} (10))

Remove parentheses:

(- a) = - a

= - (lo g_{10} (424) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (424) - 3)

Distribute parentheses

= - (lo g_{10} (424)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (424) + 3

- 4 (ln (4) - ln (8))

ln (\frac{ln ( 0.2 )}{ln ( 0.8 )})

ln (\frac{e ^{3}}{17})

ln (7 \cdot e^{- x + 5})

ln (\frac{1}{4 x} \cdot e^{\frac{- 1}{2}})

What is simplify-log_{10}(424*10^{(-3)}) ?
The solution to simplify-log_{10}(424*10^{(-3)}) is -log_{10}(424)+3