What is simplify-log_{10}(3.49*10^{-3}) ?

The solution to simplify-log_{10}(3.49*10^{-3}) is -log_{10}(3.49)+3

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simplify-log_{10}(3.49*10^{-3})

simplify

- lo g_{10} (3.49 \cdot 1 0^{- 3})

- lo g_{10} (3.49) + 3

Decimal Notation

2.45717 \dots

Solution steps

- lo g_{10} (3.49 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (3.49 \cdot 1 0^{- 3}) = lo g_{10} (3.49) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (3.49) + 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} (3.49) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (3.49) - 3)

Distribute parentheses

= - (lo g_{10} (3.49)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (3.49) + 3

ln (2 \cdot x) - x^{2} + 5

ln (\frac{66}{51}) \cdot 5

ln (r) + ln (t) + ln (r)

ln (1.05 - 0.2 v) - ln (- 0.55)

ln (\frac{( x + 2 )}{x - 1})

What is simplify-log_{10}(3.49*10^{-3}) ?
The solution to simplify-log_{10}(3.49*10^{-3}) is -log_{10}(3.49)+3