What is simplify-log_{10}(1.7*10^{-4}) ?

The solution to simplify-log_{10}(1.7*10^{-4}) is -log_{10}(1.7)+4

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simplify-log_{10}(1.7*10^{-4})

simplify

- lo g_{10} (1.7 \cdot 1 0^{- 4})

- lo g_{10} (1.7) + 4

Decimal Notation

3.76955 \dots

Solution steps

- lo g_{10} (1.7 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (1.7 \cdot 1 0^{- 4}) = lo g_{10} (1.7) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (1.7) + 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} (1.7) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (1.7) - 4)

Distribute parentheses

= - (lo g_{10} (1.7)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (1.7) + 4

ln (- x e^{x})

6 lo g_{10} (y) + 3 lo g_{10} (x)

lo g_{b} (\frac{1}{x})

\frac{1}{3} ln (x) + \frac{10}{12} ln (x + 3) - \frac{1}{6} ln (x + 3)

ln (\frac{350}{400 - x})

What is simplify-log_{10}(1.7*10^{-4}) ?
The solution to simplify-log_{10}(1.7*10^{-4}) is -log_{10}(1.7)+4