What is simplify-log_{10}(3*10^{-8}) ?

The solution to simplify-log_{10}(3*10^{-8}) is -log_{10}(3)+8

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simplify-log_{10}(3*10^{-8})

simplify

- lo g_{10} (3 \cdot 1 0^{- 8})

- lo g_{10} (3) + 8

Decimal Notation

7.52287 \dots

Solution steps

- lo g_{10} (3 \cdot 1 0^{- 8})

Apply log rule:

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

lo g_{10} (3 \cdot 1 0^{- 8}) = lo g_{10} (3) + lo g_{10} (1 0^{- 8})

= - (lo g_{10} (3) + 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) - 8 lo g_{10} (10))

8 lo g_{10} (10) = 8

= - (lo g_{10} (3) - 8)

Distribute parentheses

= - (lo g_{10} (3)) - (- 8)

Apply minus-plus rules

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

= - lo g_{10} (3) + 8

lo g_{8} (5) + lo g_{8} (7)

lo g_{b} (b) - \frac{1}{3} lo g_{b} (y) + \frac{1}{4} lo g_{b} (z)

ln^{2} (3 x)

lo g_{10} (x^{2} - 9) - lo g_{10} (x^{2} + 7 x + 12)

lo g_{3} (\frac{27}{x + 6})

What is simplify-log_{10}(3*10^{-8}) ?
The solution to simplify-log_{10}(3*10^{-8}) is -log_{10}(3)+8