What is simplify-log_{10}(4*10^{-6}) ?

The solution to simplify-log_{10}(4*10^{-6}) is -2log_{10}(2)+6

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simplify-log_{10}(4*10^{-6})

simplify

- lo g_{10} (4 \cdot 1 0^{- 6})

- 2 lo g_{10} (2) + 6

Decimal Notation

5.39794 \dots

Solution steps

- lo g_{10} (4 \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (4 \cdot 1 0^{- 6}) = lo g_{10} (4) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (4) + lo g_{10} (1 0^{- 6}))

Apply log rule:

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

lo g_{10} (1 0^{- 6}) = - 6 lo g_{10} (10)

= - (lo g_{10} (4) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (4) - 6)

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

= - (2 lo g_{10} (2) - 6)

Distribute parentheses

= - (2 lo g_{10} (2)) - (- 6)

Apply minus-plus rules

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

= - 2 lo g_{10} (2) + 6

- ln (\frac{4}{3})

\frac{1}{2} ln (\frac{3}{4}) - \frac{1}{2} ln (\frac{1}{2})

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

5 lo g_{5} (7 y + 1) + \frac{1}{2} lo g_{5} (y + 5)

ln (\frac{2 x}{a ^{2}})

What is simplify-log_{10}(4*10^{-6}) ?
The solution to simplify-log_{10}(4*10^{-6}) is -2log_{10}(2)+6