What is simplify-log_{10}(9\times 10^{-5}) ?

The solution to simplify-log_{10}(9\times 10^{-5}) is -2log_{10}(3)+5

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simplify-log_{10}(9\times 10^{-5})

simplify

- lo g_{10} (9 \cdot 1 0^{- 5})

- 2 lo g_{10} (3) + 5

Decimal Notation

4.04575 \dots

Solution steps

- lo g_{10} (9 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (9 \cdot 1 0^{- 5}) = lo g_{10} (9) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (9) + 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} (9) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (9) - 5)

lo g_{10} (9) = 2 lo g_{10} (3)

= - (2 lo g_{10} (3) - 5)

Distribute parentheses

= - (2 lo g_{10} (3)) - (- 5)

Apply minus-plus rules

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

= - 2 lo g_{10} (3) + 5

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

\frac{1}{5} ln (3)

lo g_{\frac{a}{2}} (\frac{a ^{2}}{4})

lo g_{5} (7) + lo g_{5} (2)

What is simplify-log_{10}(9\times 10^{-5}) ?
The solution to simplify-log_{10}(9\times 10^{-5}) is -2log_{10}(3)+5