What is simplify-log_{10}(9.6*10^{-4}) ?

The solution to simplify-log_{10}(9.6*10^{-4}) is -log_{10}(9.6)+4

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simplify-log_{10}(9.6*10^{-4})

simplify

- lo g_{10} (9.6 \cdot 1 0^{- 4})

- lo g_{10} (9.6) + 4

Decimal Notation

3.01772 \dots

Solution steps

- lo g_{10} (9.6 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (9.6 \cdot 1 0^{- 4}) = lo g_{10} (9.6) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (9.6) + 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} (9.6) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (9.6) - 4)

Distribute parentheses

= - (lo g_{10} (9.6)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (9.6) + 4

ln ∣ p ∣ - ln ∣ o ∣

lo g_{10} (2 π \cdot 400.2 \cdot 5.03 \cdot 9.566)

ln (\frac{113}{5})

\frac{3}{2} ln (4 x^{6}) - \frac{4}{5} ln (2 y^{10})

0.5 ln (\frac{10.5}{6.5})

What is simplify-log_{10}(9.6*10^{-4}) ?
The solution to simplify-log_{10}(9.6*10^{-4}) is -log_{10}(9.6)+4