What is simplify-log_{10}(4*10^{-10}) ?

The solution to simplify-log_{10}(4*10^{-10}) is -2log_{10}(2)+10

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simplify-log_{10}(4*10^{-10})

simplify

- lo g_{10} (4 \cdot 1 0^{- 10})

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

Decimal

9.39794 \dots

Solution steps

- lo g_{10} (4 \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (4 \cdot 1 0^{- 10}) = lo g_{10} (4) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (4) + 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} (4) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (4) - 10)

lo g_{10} (4) = 2 lo g_{10} (2)

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

Distribute parentheses

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

Apply minus-plus rules

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

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

lo g_{8} (6) + lo g_{8} (x)

lo g_{10} (\frac{x ^{5}}{z 3 y ^{2}})

tanh (\frac{1}{2} ln (\frac{1 + z}{1 - z}))

2 lo g_{10} (2) + 4 lo g_{10} (3)

lo g_{10} (k) - 5 lo g_{10} (g)

What is simplify-log_{10}(4*10^{-10}) ?
The solution to simplify-log_{10}(4*10^{-10}) is -2log_{10}(2)+10