What is simplify-log_{10}(1.8x10^{-3}) ?

The solution to simplify-log_{10}(1.8x10^{-3}) is -log_{10}(1.8)-log_{10}(x)+3

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simplify-log_{10}(1.8x10^{-3})

simplify

- lo g_{10} (1.8 x 1 0^{- 3})

- lo g_{10} (1.8) - lo g_{10} (x) + 3

Solution steps

- lo g_{10} (1.8 x \cdot 1 0^{- 3})

Apply log rule:

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

lo g_{10} (1.8 x \cdot 1 0^{- 3}) = lo g_{10} (1.8) + lo g_{10} (x) + lo g_{10} (1 0^{- 3})

= - (lo g_{10} (x) + lo g_{10} (1.8) + lo g_{10} (1 0^{- 3}))

Apply log rule:

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

lo g_{10} (1 0^{- 3}) = - 3 lo g_{10} (10)

= - (lo g_{10} (1.8) + lo g_{10} (x) - 3 lo g_{10} (10))

3 lo g_{10} (10) = 3

= - (lo g_{10} (x) + lo g_{10} (1.8) - 3)

Distribute parentheses

= - (lo g_{10} (1.8)) - (lo g_{10} (x)) - (- 3)

Apply minus-plus rules

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

= - lo g_{10} (1.8) - lo g_{10} (x) + 3

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

\frac{1}{3} ln ∣ x - 1 ∣ - \frac{1}{3} ln ∣ x + 2 ∣ + C

4 ln (2 y) + 2 ln (y)

ln (2 ∣ ln (x) ∣)

ln (\frac{330}{293})

What is simplify-log_{10}(1.8x10^{-3}) ?
The solution to simplify-log_{10}(1.8x10^{-3}) is -log_{10}(1.8)-log_{10}(x)+3