What is simplify-log_{10}(3.1*10^{-5}) ?

The solution to simplify-log_{10}(3.1*10^{-5}) is -log_{10}(3.1)+5

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simplify-log_{10}(3.1*10^{-5})

simplify

- lo g_{10} (3.1 \cdot 1 0^{- 5})

- lo g_{10} (3.1) + 5

Decimal Notation

4.50863 \dots

Solution steps

- lo g_{10} (3.1 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (3.1 \cdot 1 0^{- 5}) = lo g_{10} (3.1) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (3.1) + lo g_{10} (1 0^{- 5}))

Apply log rule:

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

lo g_{10} (1 0^{- 5}) = - 5 lo g_{10} (10)

= - (lo g_{10} (3.1) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (3.1) - 5)

Distribute parentheses

= - (lo g_{10} (3.1)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (3.1) + 5

lo g_{5} (\frac{5}{7}) + lo g_{5} (\frac{49}{25})

lo g_{4} (\frac{7}{19}) + lo g_{4} (\frac{19}{7})

7 lo g_{6} (x - 2) + 2 lo g_{6} (3 x)

lo g_{10} (0.0001) - lo g_{10} (0.1)

4 lo g_{10} (x) + 3 lo g_{10} (y)

What is simplify-log_{10}(3.1*10^{-5}) ?
The solution to simplify-log_{10}(3.1*10^{-5}) is -log_{10}(3.1)+5