What is simplify-log_{10}(2*10^{-6}) ?

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

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simplify-log_{10}(2*10^{-6})

simplify

- lo g_{10} (2 \cdot 1 0^{- 6})

- lo g_{10} (2) + 6

Decimal Notation

5.69897 \dots

Solution steps

- lo g_{10} (2 \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (2 \cdot 1 0^{- 6}) = lo g_{10} (2) + lo g_{10} (1 0^{- 6})

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

6 lo g_{10} (10) = 6

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

Distribute parentheses

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

Apply minus-plus rules

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

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

ln (\frac{e ^{4}}{10})

- 3 (\frac{1}{2} ln (2^{2} - 9) - \frac{1}{2} ln ((- 2)^{2} - 9))

- lo g_{10} (2.5 \cdot 1 0^{- 3})

lo g_{10} (lo g_{10} (10000 0^{2 x}))

\frac{ln ( \frac{9}{1024} )}{2 ln ( \frac{243}{16} )}

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