What is simplify-log_{10}(3\times 10^{-5}) ?

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

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simplify-log_{10}(3\times 10^{-5})

simplify

- lo g_{10} (3 \cdot 1 0^{- 5})

- lo g_{10} (3) + 5

Decimal Notation

4.52287 \dots

Solution steps

- lo g_{10} (3 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (3 \cdot 1 0^{- 5}) = lo g_{10} (3) + lo g_{10} (1 0^{- 5})

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

5 lo g_{10} (10) = 5

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

Distribute parentheses

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

Apply minus-plus rules

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

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

ln (\frac{2 x ^{3} y ^{3} - 1}{z ^{5}})

lo g_{6} (\frac{16 x ^{2}}{2 x - 4})

lo g_{7} (\frac{x ^{4}}{y ^{2}})

lo g_{2} (\frac{4}{x + 9})

lo g_{10} (y) + 2 lo g_{10} (z)

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