What is simplify-log_{10}(8.56*10^{-4}) ?

The solution to simplify-log_{10}(8.56*10^{-4}) is -log_{10}(8.56)+4

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simplify-log_{10}(8.56*10^{-4})

simplify

- lo g_{10} (8.56 \cdot 1 0^{- 4})

- lo g_{10} (8.56) + 4

Decimal Notation

3.06752 \dots

Solution steps

- lo g_{10} (8.56 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (8.56 \cdot 1 0^{- 4}) = lo g_{10} (8.56) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (8.56) + 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} (8.56) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (8.56) - 4)

Distribute parentheses

= - (lo g_{10} (8.56)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (8.56) + 4

ln (\frac{1 0 ^{25}}{1.5})

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

\frac{1}{3} ln (x + 1) + \frac{8}{3} ln (x - 2)

lo g_{10} (\frac{x ^{9}}{y ^{4}})

ln (\frac{3}{e ^{3}})

What is simplify-log_{10}(8.56*10^{-4}) ?
The solution to simplify-log_{10}(8.56*10^{-4}) is -log_{10}(8.56)+4