What is simplify-log_{10}(5(10^{-6})) ?

The solution to simplify-log_{10}(5(10^{-6})) is -log_{10}(5)+6

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simplify-log_{10}(5(10^{-6}))

simplify

- lo g_{10} (5 (1 0^{- 6}))

- lo g_{10} (5) + 6

Decimal

5.30102 \dots

Solution steps

- lo g_{10} (5 (1 0^{- 6}))

Apply log rule:

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

lo g_{10} (5 (1 0^{- 6})) = lo g_{10} (5) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (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} (5) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (5) - 6)

Distribute parentheses

= - (lo g_{10} (5)) - (- 6)

Apply minus-plus rules

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

= - lo g_{10} (5) + 6

ln (\frac{- 0.375}{( - 0.375 ) ^{3} - 8}) + 3

\frac{1}{3} \cdot ln (1 + 2 \cdot 100) + \frac{2}{3} \cdot ln (1 + 2 \cdot 400)

- ln (\frac{131}{441.00049})

[ln (- 1) - ln (- 2)]

ln (\frac{x}{n})

What is simplify-log_{10}(5(10^{-6})) ?
The solution to simplify-log_{10}(5(10^{-6})) is -log_{10}(5)+6