What is simplify-log_{10}(4*10^{-5}) ?

The solution to simplify-log_{10}(4*10^{-5}) is -2log_{10}(2)+5

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simplify-log_{10}(4*10^{-5})

simplify

- lo g_{10} (4 \cdot 1 0^{- 5})

- 2 lo g_{10} (2) + 5

Decimal Notation

4.39794 \dots

Solution steps

- lo g_{10} (4 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (4 \cdot 1 0^{- 5}) = lo g_{10} (4) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (4) + 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} (4) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (4) - 5)

lo g_{10} (4) = 2 lo g_{10} (2)

= - (2 lo g_{10} (2) - 5)

Distribute parentheses

= - (2 lo g_{10} (2)) - (- 5)

Apply minus-plus rules

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

= - 2 lo g_{10} (2) + 5

2 lo g_{10} (8) + lo g_{10} (9) - lo g_{10} (36)

lo g_{b} (\frac{5}{3})

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

lo g_{10} (\frac{u}{v})

lo g_{2} (5) - lo g_{2} (3)

What is simplify-log_{10}(4*10^{-5}) ?
The solution to simplify-log_{10}(4*10^{-5}) is -2log_{10}(2)+5