What is simplify-log_{10}(1.1*10^{-4}) ?

The solution to simplify-log_{10}(1.1*10^{-4}) is -log_{10}(1.1)+4

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simplify-log_{10}(1.1*10^{-4})

simplify

- lo g_{10} (1.1 \cdot 1 0^{- 4})

- lo g_{10} (1.1) + 4

Decimal Notation

3.95860 \dots

Solution steps

- lo g_{10} (1.1 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (1.1 \cdot 1 0^{- 4}) = lo g_{10} (1.1) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (1.1) + lo g_{10} (1 0^{- 4}))

Apply log rule:

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

lo g_{10} (1 0^{- 4}) = - 4 lo g_{10} (10)

= - (lo g_{10} (1.1) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (1.1) - 4)

Distribute parentheses

= - (lo g_{10} (1.1)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (1.1) + 4

ln (\frac{950}{1150})

ln (x^{2}) - ln (x^{4}) - 3 x

ln (0.198 10)

ln (\frac{e ^{9}}{2})

ln (x ln (2))

What is simplify-log_{10}(1.1*10^{-4}) ?
The solution to simplify-log_{10}(1.1*10^{-4}) is -log_{10}(1.1)+4