What is simplify-log_{10}(9*10^{-10}) ?

The solution to simplify-log_{10}(9*10^{-10}) is -2log_{10}(3)+10

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simplify-log_{10}(9*10^{-10})

simplify

- lo g_{10} (9 \cdot 1 0^{- 10})

- 2 lo g_{10} (3) + 10

Decimal Notation

9.04575 \dots

Solution steps

- lo g_{10} (9 \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (9 \cdot 1 0^{- 10}) = lo g_{10} (9) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (9) + 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} (9) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (9) - 10)

lo g_{10} (9) = 2 lo g_{10} (3)

= - (2 lo g_{10} (3) - 10)

Distribute parentheses

= - (2 lo g_{10} (3)) - (- 10)

Apply minus-plus rules

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

= - 2 lo g_{10} (3) + 10

ln (1 - 2 y) - ln (1 - y)

lo g_{3} (\frac{1}{9 ∣ 49})

lo g_{10} (0.5) - lo g_{10} (x)

ln (\frac{8.74}{12})

x + ln (2 x)

What is simplify-log_{10}(9*10^{-10}) ?
The solution to simplify-log_{10}(9*10^{-10}) is -2log_{10}(3)+10