What is simplify-log_{10}(1.866*10^{-10}) ?

The solution to simplify-log_{10}(1.866*10^{-10}) is -log_{10}(1.866)+10

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simplify-log_{10}(1.866*10^{-10})

simplify

- lo g_{10} (1.866 \cdot 1 0^{- 10})

- lo g_{10} (1.866) + 10

Decimal Notation

9.72908 \dots

Solution steps

- lo g_{10} (1.866 \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (1.866 \cdot 1 0^{- 10}) = lo g_{10} (1.866) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (1.866) + lo g_{10} (1 0^{- 10}))

Apply log rule:

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

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

= - (lo g_{10} (1.866) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (1.866) - 10)

Distribute parentheses

= - (lo g_{10} (1.866)) - (- 10)

Apply minus-plus rules

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

= - lo g_{10} (1.866) + 10

ln (\frac{50}{21.026})

lo g_{2^{- \frac{1}{2}}} (\frac{8}{5 + 11})

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

lo g_{8} (x \cdot y \cdot z^{5})

\frac{3}{2} ln ∣ 4 + 3 ∣ + \frac{1}{2} ln ∣ x - 3 ∣

What is simplify-log_{10}(1.866*10^{-10}) ?
The solution to simplify-log_{10}(1.866*10^{-10}) is -log_{10}(1.866)+10