What is simplify-log_{10}(2.9*10^{-3}) ?

The solution to simplify-log_{10}(2.9*10^{-3}) is -log_{10}(2.9)+3

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simplify-log_{10}(2.9*10^{-3})

simplify

- lo g_{10} (2.9 \cdot 1 0^{- 3})

- lo g_{10} (2.9) + 3

Decimal Notation

2.53760 \dots

Solution steps

- lo g_{10} (2.9 \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (2.9 \cdot 1 0^{- 3}) = lo g_{10} (2.9) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (2.9) + 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} (2.9) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (2.9) - 3)

Distribute parentheses

= - (lo g_{10} (2.9)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (2.9) + 3

2 ln (3) - ln (2) - 2 ln (2)

- lo g_{10} (2 \cdot 1 0^{- 1})

4 lo g_{5} (x) - 3 lo g_{5} (y)

0.026 ln (0.095) + 0.416 ln (10)

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

What is simplify-log_{10}(2.9*10^{-3}) ?
The solution to simplify-log_{10}(2.9*10^{-3}) is -log_{10}(2.9)+3