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

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

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

simplify

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

- 2 lo g_{10} (3) + 9

Decimal Notation

8.04575 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

9 lo g_{10} (10) = 9

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

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

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

Distribute parentheses

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

Apply minus-plus rules

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

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

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- \frac{3}{4} lo g_{e} (\frac{3}{4}) - \frac{1}{4} lo g_{e} (\frac{1}{4})

ln (41) - ln (5) - ln (2)

lo g_{7} (\frac{ln ( 0.25 )}{ln ( 0.75 )})

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