What is simplify-log_{10}(5.7*10^{-4}) ?

The solution to simplify-log_{10}(5.7*10^{-4}) is -log_{10}(5.7)+4

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simplify-log_{10}(5.7*10^{-4})

simplify

- lo g_{10} (5.7 \cdot 1 0^{- 4})

- lo g_{10} (5.7) + 4

Decimal Notation

3.24412 \dots

Solution steps

- lo g_{10} (5.7 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (5.7 \cdot 1 0^{- 4}) = lo g_{10} (5.7) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (5.7) + 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} (5.7) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (5.7) - 4)

Distribute parentheses

= - (lo g_{10} (5.7)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (5.7) + 4

lo g_{3} (11 p^{3})

5 ln (\frac{3}{4}) + \frac{5 - 3 ln ( \frac{81}{64} )}{2}

ln (10 x + 3) + ln (x + 3)

ln ((\frac{1}{2} + \frac{x}{4})^{a} \cdot (\frac{1}{4} - \frac{x}{4})^{b + c} \cdot (\frac{x}{4})^{d})

\frac{3}{4} lo g_{8} (18)

What is simplify-log_{10}(5.7*10^{-4}) ?
The solution to simplify-log_{10}(5.7*10^{-4}) is -log_{10}(5.7)+4