What is simplify-log_{10}(7.1*10^{-10}) ?

The solution to simplify-log_{10}(7.1*10^{-10}) is -log_{10}(7.1)+10

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simplify-log_{10}(7.1*10^{-10})

simplify

- lo g_{10} (7.1 \cdot 1 0^{- 10})

- lo g_{10} (7.1) + 10

Decimal Notation

9.14874 \dots

Solution steps

- lo g_{10} (7.1 \cdot 1 0^{- 10})

Apply log rule:

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

lo g_{10} (7.1 \cdot 1 0^{- 10}) = lo g_{10} (7.1) + lo g_{10} (1 0^{- 10})

= - (lo g_{10} (7.1) + 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} (7.1) - 10 lo g_{10} (10))

10 lo g_{10} (10) = 10

= - (lo g_{10} (7.1) - 10)

Distribute parentheses

= - (lo g_{10} (7.1)) - (- 10)

Apply minus-plus rules

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

= - lo g_{10} (7.1) + 10

lo g_{a} (x) - 3 lo g_{a} (x - y) - \frac{1}{2} lo g_{a} (x)

lo g_{6} (\frac{x ^{7} ( x + 9 )}{( x - 4 ) ^{5}})

ln (x^{2} (x + 6)^{7} (x^{2} + 5)^{4})

1004 \cdot ln (\frac{100}{930}) - 287 \cdot ln (\frac{3}{4})

20 lo g_{10} (\frac{2 \cdot 1 0 ^{- 5}}{1 0 ^{- 6}})

What is simplify-log_{10}(7.1*10^{-10}) ?
The solution to simplify-log_{10}(7.1*10^{-10}) is -log_{10}(7.1)+10