What is simplify-log_{10}(6.2*10^{-5}) ?

The solution to simplify-log_{10}(6.2*10^{-5}) is -log_{10}(6.2)+5

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simplify-log_{10}(6.2*10^{-5})

simplify

- lo g_{10} (6.2 \cdot 1 0^{- 5})

- lo g_{10} (6.2) + 5

Decimal Notation

4.20760 \dots

Solution steps

- lo g_{10} (6.2 \cdot 1 0^{- 5})

Apply log rule:

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

lo g_{10} (6.2 \cdot 1 0^{- 5}) = lo g_{10} (6.2) + lo g_{10} (1 0^{- 5})

= - (lo g_{10} (6.2) + 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} (6.2) - 5 lo g_{10} (10))

5 lo g_{10} (10) = 5

= - (lo g_{10} (6.2) - 5)

Distribute parentheses

= - (lo g_{10} (6.2)) - (- 5)

Apply minus-plus rules

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

= - lo g_{10} (6.2) + 5

0.0259 \cdot ln (\frac{4 \cdot 1 0 ^{12}}{1.5 \cdot 1 0 ^{10}})

ln (\frac{32}{5})

lo g_{10} (4 x^{3}) - \frac{1}{2} lo g_{10} ((x + 3) (x - 2))

lo g_{2} ((x yz)^{3})

3 ln (a^{2}) - 3 ln (b) + \frac{1}{3} ln (c)

What is simplify-log_{10}(6.2*10^{-5}) ?
The solution to simplify-log_{10}(6.2*10^{-5}) is -log_{10}(6.2)+5