What is simplify-log_{10}(6.667*10^{-5}) ?

The solution to simplify-log_{10}(6.667*10^{-5}) is -log_{10}(6.667)+5

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simplify-log_{10}(6.667*10^{-5})

simplify

- lo g_{10} (6.667 \cdot 1 0^{- 5})

- lo g_{10} (6.667) + 5

Decimal Notation

4.17606 \dots

Solution steps

- lo g_{10} (6.667 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (6.667 \cdot 1 0^{- 5}) = lo g_{10} (6.667) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (6.667) + 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} (6.667) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (6.667) - 5)

Distribute parentheses

= - (lo g_{10} (6.667)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (6.667) + 5

ln (\frac{e ^{- B A}}{1 - e ^{- B A}})

5 lo g_{2} (x) - 3 lo g_{2} (z)

ln (5 x^{4} y)

ln (\frac{x + 2 y}{3 + x z})

ln ((\frac{a}{b})^{n} (x)^{n (a - b)})

What is simplify-log_{10}(6.667*10^{-5}) ?
The solution to simplify-log_{10}(6.667*10^{-5}) is -log_{10}(6.667)+5