What is simplify-log_{10}(4.24*10^{-3}) ?

The solution to simplify-log_{10}(4.24*10^{-3}) is -log_{10}(4.24)+3

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simplify-log_{10}(4.24*10^{-3})

simplify

- lo g_{10} (4.24 \cdot 1 0^{- 3})

- lo g_{10} (4.24) + 3

Decimal Notation

2.37263 \dots

Solution steps

- lo g_{10} (4.24 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (4.24 \cdot 1 0^{- 3}) = lo g_{10} (4.24) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (4.24) + 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} (4.24) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (4.24) - 3)

Distribute parentheses

= - (lo g_{10} (4.24)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (4.24) + 3

lo g_{10} (y x^{9})

ln (7) + ln (x)

lo g_{10} (\frac{x ^{5}}{y ^{2}})

lo g_{10} (x^{2} + 2 x - 15) - lo g_{10} (x^{2} - 7 x + 12)

lo g_{a} (40) + lo g_{a} (4)

What is simplify-log_{10}(4.24*10^{-3}) ?
The solution to simplify-log_{10}(4.24*10^{-3}) is -log_{10}(4.24)+3