What is simplify-log_{10}(4*10^{-8}) ?

The solution to simplify-log_{10}(4*10^{-8}) is -2log_{10}(2)+8

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simplify-log_{10}(4*10^{-8})

simplify

- lo g_{10} (4 \cdot 1 0^{- 8})

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

Decimal Notation

7.39794 \dots

Solution steps

- lo g_{10} (4 \cdot 1 0^{- 8})

Apply log rule:

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

lo g_{10} (4 \cdot 1 0^{- 8}) = lo g_{10} (4) + lo g_{10} (1 0^{- 8})

= - (lo g_{10} (4) + 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} (4) - 8 lo g_{10} (10))

8 lo g_{10} (10) = 8

= - (lo g_{10} (4) - 8)

lo g_{10} (4) = 2 lo g_{10} (2)

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

Distribute parentheses

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

Apply minus-plus rules

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

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

lo g_{10} (5) - lo g_{10} (2)

lo g_{10} (\frac{3 a ^{2} b c}{2})

ln (\frac{a ^{- 2}}{b ^{- 4} c ^{5}})

lo g_{7} (u) + 6 lo g_{7} (v)

lo g_{10} (\frac{2 x}{5})

What is simplify-log_{10}(4*10^{-8}) ?
The solution to simplify-log_{10}(4*10^{-8}) is -2log_{10}(2)+8