What is simplify-log_{10}(8*10^{-4}) ?

The solution to simplify-log_{10}(8*10^{-4}) is -3log_{10}(2)+4

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simplify-log_{10}(8*10^{-4})

simplify

- lo g_{10} (8 \cdot 1 0^{- 4})

- 3 lo g_{10} (2) + 4

Decimal Notation

3.09691 \dots

Solution steps

- lo g_{10} (8 \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (8 \cdot 1 0^{- 4}) = lo g_{10} (8) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (8) + 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) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (8) - 4)

lo g_{10} (8) = 3 lo g_{10} (2)

= - (3 lo g_{10} (2) - 4)

Distribute parentheses

= - (3 lo g_{10} (2)) - (- 4)

Apply minus-plus rules

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

= - 3 lo g_{10} (2) + 4

3 lo g_{6} (x) - 2 lo g_{6} (y)

0.3 ln (\frac{10 + 104}{2})

ln (\frac{2 x ^{4}}{y ^{7}})

ln (\frac{0.525}{0.412})

- lo g_{10} (2.17 \cdot 1 0^{- 9})

What is simplify-log_{10}(8*10^{-4}) ?
The solution to simplify-log_{10}(8*10^{-4}) is -3log_{10}(2)+4