What is simplify-log_{10}(3.2*10^{-8}) ?

The solution to simplify-log_{10}(3.2*10^{-8}) is -log_{10}(3.2)+8

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simplify-log_{10}(3.2*10^{-8})

simplify

- lo g_{10} (3.2 \cdot 1 0^{- 8})

- lo g_{10} (3.2) + 8

Decimal Notation

7.49485 \dots

Solution steps

- lo g_{10} (3.2 \cdot 1 0^{- 8})

Apply log rule:

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

lo g_{10} (3.2 \cdot 1 0^{- 8}) = lo g_{10} (3.2) + lo g_{10} (1 0^{- 8})

= - (lo g_{10} (3.2) + lo g_{10} (1 0^{- 8}))

Apply log rule:

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

lo g_{10} (1 0^{- 8}) = - 8 lo g_{10} (10)

= - (lo g_{10} (3.2) - 8 lo g_{10} (10))

8 lo g_{10} (10) = 8

= - (lo g_{10} (3.2) - 8)

Distribute parentheses

= - (lo g_{10} (3.2)) - (- 8)

Apply minus-plus rules

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

= - lo g_{10} (3.2) + 8

- lo g_{10} (1.1 \cdot 1 0^{- 6})

- 2 (ln (100 - x) - 2 ln (10))

4 lo g_{10} (x - 9) - 5 lo g_{10} (x)

6 lo g_{10} (x) + 7 lo g_{10} (y)

ln (\frac{x ^{2} + y ^{2}}{x + y}) - ln (x + y)

What is simplify-log_{10}(3.2*10^{-8}) ?
The solution to simplify-log_{10}(3.2*10^{-8}) is -log_{10}(3.2)+8