What is simplify-log_{10}(3.4*10^{-5}) ?

The solution to simplify-log_{10}(3.4*10^{-5}) is -log_{10}(3.4)+5

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simplify-log_{10}(3.4*10^{-5})

simplify

- lo g_{10} (3.4 \cdot 1 0^{- 5})

- lo g_{10} (3.4) + 5

Decimal Notation

4.46852 \dots

Solution steps

- lo g_{10} (3.4 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (3.4 \cdot 1 0^{- 5}) = lo g_{10} (3.4) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (3.4) + lo g_{10} (1 0^{- 5}))

Apply log rule:

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

lo g_{10} (1 0^{- 5}) = - 5 lo g_{10} (10)

= - (lo g_{10} (3.4) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (3.4) - 5)

Distribute parentheses

= - (lo g_{10} (3.4)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (3.4) + 5

\frac{ln ( 77 ) - 12 ln ( 2 )}{12 ln ( 2 )}

ln (\frac{1 \cdot 1 0 ^{- 4}}{1 \cdot 1 0 ^{- 3}})

lo g_{v} (b^{4}) (b^{9})

lo g_{6} ((\frac{u}{v ^{6}})^{5})

- ln (1 - x) + ln (1 - y)

What is simplify-log_{10}(3.4*10^{-5}) ?
The solution to simplify-log_{10}(3.4*10^{-5}) is -log_{10}(3.4)+5