What is simplify-log_{10}(1.1004*10^{-10}) ?

The solution to simplify-log_{10}(1.1004*10^{-10}) is -log_{10}(1.1004)+10

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simplify-log_{10}(1.1004*10^{-10})

simplify

- lo g_{10} (1.1004 \cdot 1 0^{- 10})

- lo g_{10} (1.1004) + 10

Decimal Notation

9.95844 \dots

Solution steps

- lo g_{10} (1.1004 \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (1.1004 \cdot 1 0^{- 10}) = lo g_{10} (1.1004) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (1.1004) + 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} (1.1004) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (1.1004) - 10)

Distribute parentheses

= - (lo g_{10} (1.1004)) - (- 10)

Apply minus-plus rules

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

= - lo g_{10} (1.1004) + 10

3.86 + lo g_{10} (\frac{0.004}{0.021})

ln (a X^{b} Y^{c})

\frac{1}{2} ln ∣ 2 (9) + 1 ∣ + 2 ln ∣ 9 - 1 ∣

ln (\frac{1643.85}{547.85}) \cdot 8

ln (\frac{3.1416}{3})

What is simplify-log_{10}(1.1004*10^{-10}) ?
The solution to simplify-log_{10}(1.1004*10^{-10}) is -log_{10}(1.1004)+10