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

The solution to simplify-log_{10}(8*10^{-8}) is -3log_{10}(2)+8

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

simplify

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

- 3 lo g_{10} (2) + 8

Decimal Notation

7.09691 \dots

Solution steps

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

Apply log rule:

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

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

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

8 lo g_{10} (10) = 8

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

lo g_{10} (8) = 3 lo g_{10} (2)

= - (3 lo g_{10} (2) - 8)

Distribute parentheses

= - (3 lo g_{10} (2)) - (- 8)

Apply minus-plus rules

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

= - 3 lo g_{10} (2) + 8

lo g_{10} (\frac{1 0 ^{x}}{x ( x ^{2} + 1 ) ( x ^{4} + 2 )})

5 ln (x) + 2 ln (y)

- lo g_{10} (4.2 \times 1 0^{- 3})

- ln (x + 2) + 2 ln (x + 3)

2 lo g_{5} (3 x + 2) - lo g_{5} (x + 1)

What is simplify-log_{10}(8*10^{-8}) ?
The solution to simplify-log_{10}(8*10^{-8}) is -3log_{10}(2)+8