What is simplify-log_{10}(3.4*10^{-3}) ?

The solution to simplify-log_{10}(3.4*10^{-3}) is -log_{10}(3.4)+3

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simplify-log_{10}(3.4*10^{-3})

simplify

- lo g_{10} (3.4 \cdot 1 0^{- 3})

- lo g_{10} (3.4) + 3

Decimal Notation

2.46852 \dots

Solution steps

- lo g_{10} (3.4 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (3.4 \cdot 1 0^{- 3}) = lo g_{10} (3.4) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (3.4) + 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} (3.4) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (3.4) - 3)

Distribute parentheses

= - (lo g_{10} (3.4)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (3.4) + 3

2 ln (\frac{4}{7})

ln (\frac{1}{7 x - 3})

ln (a - b) - ln (a + b) + 2 ln (c)

32 ln (\frac{7}{5}) - 8

4 ln (4) - 6 ln (3) + 2 ln (2) - 2

What is simplify-log_{10}(3.4*10^{-3}) ?
The solution to simplify-log_{10}(3.4*10^{-3}) is -log_{10}(3.4)+3