What is simplify-log_{10}(8.5x10^{-6}) ?

The solution to simplify-log_{10}(8.5x10^{-6}) is -log_{10}(8.5)-log_{10}(x)+6

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simplify-log_{10}(8.5x10^{-6})

simplify

- lo g_{10} (8.5 x 1 0^{- 6})

- lo g_{10} (8.5) - lo g_{10} (x) + 6

Solution steps

- lo g_{10} (8.5 x \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (8.5 x \cdot 1 0^{- 6}) = lo g_{10} (8.5) + lo g_{10} (x) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (x) + lo g_{10} (8.5) + 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} (8.5) + lo g_{10} (x) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (x) + lo g_{10} (8.5) - 6)

Distribute parentheses

= - (lo g_{10} (8.5)) - (lo g_{10} (x)) - (- 6)

Apply minus-plus rules

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

= - lo g_{10} (8.5) - lo g_{10} (x) + 6

10 lo g_{6} (c) + 10 lo g_{6} (a) - 2 lo g_{6} (b)

\frac{3}{5} \cdot (- \frac{2}{3} lo g_{e} (\frac{2}{3}) - \frac{1}{3} lo g_{e} (\frac{1}{3}))

3 ln (a) + ln (b) - ln (c)

ln (c e^{x})

ln (\frac{0.0573}{0.09})

What is simplify-log_{10}(8.5x10^{-6}) ?
The solution to simplify-log_{10}(8.5x10^{-6}) is -log_{10}(8.5)-log_{10}(x)+6