What is simplify-log_{10}((2)(10^{-5})) ?

The solution to simplify-log_{10}((2)(10^{-5})) is -log_{10}(2)+5

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simplify-log_{10}((2)(10^{-5}))

simplify

- lo g_{10} ((2) (1 0^{- 5}))

- lo g_{10} (2) + 5

Decimal Notation

4.69897 \dots

Solution steps

- lo g_{10} ((2) (1 0^{- 5}))

Apply log rule:

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

lo g_{10} ((2) (1 0^{- 5})) = lo g_{10} (2) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (2) + 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} (2) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (2) - 5)

Distribute parentheses

= - (lo g_{10} (2)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (2) + 5

lo g_{e} (\frac{10}{6})

lo g_{10} (x^{2} y^{4} z)

- ln (y - 1) - ln^{2} (y - 1)

ln ((- 3.5 + 0.75 x) e^{- 0, 5 x})

lo g_{4} (\frac{17}{3})

What is simplify-log_{10}((2)(10^{-5})) ?
The solution to simplify-log_{10}((2)(10^{-5})) is -log_{10}(2)+5