What is simplify-log_{10}(1.4*10^{-9}) ?

The solution to simplify-log_{10}(1.4*10^{-9}) is -log_{10}(1.4)+9

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simplify-log_{10}(1.4*10^{-9})

simplify

- lo g_{10} (1.4 \cdot 1 0^{- 9})

- lo g_{10} (1.4) + 9

Decimal Notation

8.85387 \dots

Solution steps

- lo g_{10} (1.4 \cdot 1 0^{- 9})

Apply log rule:

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

lo g_{10} (1.4 \cdot 1 0^{- 9}) = lo g_{10} (1.4) + lo g_{10} (1 0^{- 9})

= - (lo g_{10} (1.4) + 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} (1.4) - 9 lo g_{10} (10))

9 lo g_{10} (10) = 9

= - (lo g_{10} (1.4) - 9)

Distribute parentheses

= - (lo g_{10} (1.4)) - (- 9)

Apply minus-plus rules

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

= - lo g_{10} (1.4) + 9

- ln (2) + 2 (ln (7) - ln (6))

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

ln (\frac{- x}{y - 2 x})

\frac{1}{3} (ln (a) + 3 ln (b)) - \frac{1}{2} (4 ln (c) - 2 ln (d))

- \frac{1}{2} ln ∣ x + 1 ∣ + \frac{1}{2} ln ∣ x - 1 ∣ + x + C

What is simplify-log_{10}(1.4*10^{-9}) ?
The solution to simplify-log_{10}(1.4*10^{-9}) is -log_{10}(1.4)+9