What is simplify-log_{10}(4.56*10^{-5}) ?

The solution to simplify-log_{10}(4.56*10^{-5}) is -log_{10}(4.56)+5

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simplify-log_{10}(4.56*10^{-5})

simplify

- lo g_{10} (4.56 \cdot 1 0^{- 5})

- lo g_{10} (4.56) + 5

Decimal Notation

4.34103 \dots

Solution steps

- lo g_{10} (4.56 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (4.56 \cdot 1 0^{- 5}) = lo g_{10} (4.56) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (4.56) + 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} (4.56) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (4.56) - 5)

Distribute parentheses

= - (lo g_{10} (4.56)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (4.56) + 5

ln (\frac{x ^{2}}{1 - x})

\frac{ln ( x - 1 ) - ln ( x + 1 )}{2}

ln (\frac{x - 5}{x - 3})

ln (csc (θ)) + ln (tan (θ))

ln (n^{2} + 3) - ln (2 n^{2} - 1)

What is simplify-log_{10}(4.56*10^{-5}) ?
The solution to simplify-log_{10}(4.56*10^{-5}) is -log_{10}(4.56)+5