What is simplify-log_{10}(6.1*10^{-5}) ?

The solution to simplify-log_{10}(6.1*10^{-5}) is -log_{10}(6.1)+5

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simplify-log_{10}(6.1*10^{-5})

simplify

- lo g_{10} (6.1 \cdot 1 0^{- 5})

- lo g_{10} (6.1) + 5

Decimal Notation

4.21467 \dots

Solution steps

- lo g_{10} (6.1 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (6.1 \cdot 1 0^{- 5}) = lo g_{10} (6.1) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (6.1) + 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} (6.1) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (6.1) - 5)

Distribute parentheses

= - (lo g_{10} (6.1)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (6.1) + 5

ln (x^{5}) - ln (x^{3}) - 4

ln ((x - 2) (y - 2))

lo g_{e} (\frac{115}{120})

ln (2) - 2 ln (3)

ln (\frac{2000}{200})

What is simplify-log_{10}(6.1*10^{-5}) ?
The solution to simplify-log_{10}(6.1*10^{-5}) is -log_{10}(6.1)+5