What is simplify-log_{10}(2.17*10^{-9}) ?

The solution to simplify-log_{10}(2.17*10^{-9}) is -log_{10}(2.17)+9

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simplify-log_{10}(2.17*10^{-9})

simplify

- lo g_{10} (2.17 \cdot 1 0^{- 9})

- lo g_{10} (2.17) + 9

Decimal Notation

8.66354 \dots

Solution steps

- lo g_{10} (2.17 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (2.17 \cdot 1 0^{- 9}) = lo g_{10} (2.17) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (2.17) + lo g_{10} (1 0^{- 9}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{- 9}) = - 9 lo g_{10} (10)

= - (lo g_{10} (2.17) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (2.17) - 9)

Distribute parentheses

= - (lo g_{10} (2.17)) - (- 9)

Apply minus-plus rules

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

= - lo g_{10} (2.17) + 9

ln (7) - ln (14) + ln (10)

ln (x + 3) + 2 ln (y) - ln (a) + ln (b)

- lo g_{10} (8 \cdot 1 0^{- 6})

- \frac{1}{4} ln (x + 1) + \frac{1}{4} ln (x - 1)

ln (\frac{e ^{x}}{2})

What is simplify-log_{10}(2.17*10^{-9}) ?
The solution to simplify-log_{10}(2.17*10^{-9}) is -log_{10}(2.17)+9