What is simplify-log_{10}(2x10^{-10}) ?

The solution to simplify-log_{10}(2x10^{-10}) is -log_{10}(2)-log_{10}(x)+10

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simplify-log_{10}(2x10^{-10})

simplify

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

- lo g_{10} (2) - lo g_{10} (x) + 10

Solution steps

- lo g_{10} (2 x \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (2 x \cdot 1 0^{- 10}) = lo g_{10} (2) + lo g_{10} (x) + lo g_{10} (1 0^{- 10})

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

Apply log rule:

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

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

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

10 lo g_{10} (10) = 10

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

Distribute parentheses

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

Apply minus-plus rules

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

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

\frac{138}{8} (ln (68) - ln (4))

ln (3) + ln (x + 1) + (- 1)

ln (C e^{- \frac{3 t}{125}})

ln (50) - ln (180)

- 1.25 ln (\frac{50}{100})

What is simplify-log_{10}(2x10^{-10}) ?
The solution to simplify-log_{10}(2x10^{-10}) is -log_{10}(2)-log_{10}(x)+10