What is simplify-log_{10}(3.2*10^{-6}) ?

The solution to simplify-log_{10}(3.2*10^{-6}) is -log_{10}(3.2)+6

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simplify-log_{10}(3.2*10^{-6})

simplify

- lo g_{10} (3.2 \cdot 1 0^{- 6})

- lo g_{10} (3.2) + 6

Decimal Notation

5.49485 \dots

Solution steps

- lo g_{10} (3.2 \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (3.2 \cdot 1 0^{- 6}) = lo g_{10} (3.2) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (3.2) + 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} (3.2) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (3.2) - 6)

Distribute parentheses

= - (lo g_{10} (3.2)) - (- 6)

Apply minus-plus rules

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

= - lo g_{10} (3.2) + 6

\frac{1}{0.00499} ln (\frac{400 - 15}{75 - 15})

10 lo g_{10} (\frac{1 0 ^{- 6} + 1 0 ^{- 6}}{1 0 ^{- 12}})

- lo g_{10} (1.8 \cdot 1 0^{- 4}) + lo g_{10} (\frac{1}{1.5})

ln (e^{5} \cdot 3^{2 l o g_{3} (3)})

ln (\frac{m ! e ^{- x}}{( 1 + x ) ^{m + 1}})

What is simplify-log_{10}(3.2*10^{-6}) ?
The solution to simplify-log_{10}(3.2*10^{-6}) is -log_{10}(3.2)+6