What is simplify-log_{10}(2.17*10^{-6}) ?

The solution to simplify-log_{10}(2.17*10^{-6}) is -log_{10}(2.17)+6

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simplify-log_{10}(2.17*10^{-6})

simplify

- lo g_{10} (2.17 \cdot 1 0^{- 6})

- lo g_{10} (2.17) + 6

Decimal Notation

5.66354 \dots

Solution steps

- lo g_{10} (2.17 \cdot 1 0^{- 6})

Apply log rule:

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

lo g_{10} (2.17 \cdot 1 0^{- 6}) = lo g_{10} (2.17) + lo g_{10} (1 0^{- 6})

= - (lo g_{10} (2.17) + 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} (2.17) - 6 lo g_{10} (10))

6 lo g_{10} (10) = 6

= - (lo g_{10} (2.17) - 6)

Distribute parentheses

= - (lo g_{10} (2.17)) - (- 6)

Apply minus-plus rules

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

= - lo g_{10} (2.17) + 6

5 ln (x) + ln (x^{2} + 7) - 9 ln (x + 7)

lo g_{10} (3.436 + 1) - lo g_{10} (1.718)

(0.717) ln (\frac{252}{17})

ln (\frac{2 x}{3}) + \frac{1}{8} ln (\frac{x}{4}) + \frac{3}{8} ln (\frac{3 x}{4})

ln (a e^{- b x})

What is simplify-log_{10}(2.17*10^{-6}) ?
The solution to simplify-log_{10}(2.17*10^{-6}) is -log_{10}(2.17)+6