What is simplify-log_{10}(5.6*10^{-5}) ?

The solution to simplify-log_{10}(5.6*10^{-5}) is -log_{10}(5.6)+5

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simplify-log_{10}(5.6*10^{-5})

simplify

- lo g_{10} (5.6 \cdot 1 0^{- 5})

- lo g_{10} (5.6) + 5

Decimal Notation

4.25181 \dots

Solution steps

- lo g_{10} (5.6 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (5.6 \cdot 1 0^{- 5}) = lo g_{10} (5.6) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (5.6) + 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} (5.6) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (5.6) - 5)

Distribute parentheses

= - (lo g_{10} (5.6)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (5.6) + 5

lo g_{b} (x) + lo g_{b} (y)

lo g_{2} (\frac{5 y}{z})

- (\frac{2}{3} lo g_{2} (\frac{2}{3}) + \frac{1}{3} lo g_{2} (\frac{1}{3}))

lo g_{10} (1000 x^{5})

- \frac{2}{3} ln (3 y)

What is simplify-log_{10}(5.6*10^{-5}) ?
The solution to simplify-log_{10}(5.6*10^{-5}) is -log_{10}(5.6)+5