What is simplify-log_{10}(6.28*10^{-5}) ?

The solution to simplify-log_{10}(6.28*10^{-5}) is -log_{10}(6.28)+5

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simplify-log_{10}(6.28*10^{-5})

simplify

- lo g_{10} (6.28 \cdot 1 0^{- 5})

- lo g_{10} (6.28) + 5

Decimal Notation

4.20204 \dots

Solution steps

- lo g_{10} (6.28 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (6.28 \cdot 1 0^{- 5}) = lo g_{10} (6.28) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (6.28) + lo g_{10} (1 0^{- 5}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (1 0^{- 5}) = - 5 lo g_{10} (10)

= - (lo g_{10} (6.28) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (6.28) - 5)

Distribute parentheses

= - (lo g_{10} (6.28)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (6.28) + 5

lo g_{10} (4 x) - lo g_{10} (12 + x)

ln (\frac{x ^{2} - 7}{( x - 3 ) ^{4}})

ln (2 x - 1) - ln (x + 4)

lo g_{10} (4^{- 1}) + lo g_{10} (\frac{1}{2})

lo g_{10} (\frac{3 a ^{3}}{5 b})

What is simplify-log_{10}(6.28*10^{-5}) ?
The solution to simplify-log_{10}(6.28*10^{-5}) is -log_{10}(6.28)+5