What is simplify-log_{10}(7.2x10^{-4}) ?

The solution to simplify-log_{10}(7.2x10^{-4}) is -log_{10}(7.2)-log_{10}(x)+4

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simplify-log_{10}(7.2x10^{-4})

simplify

- lo g_{10} (7.2 x 1 0^{- 4})

- lo g_{10} (7.2) - lo g_{10} (x) + 4

Solution steps

- lo g_{10} (7.2 x \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (7.2 x \cdot 1 0^{- 4}) = lo g_{10} (7.2) + lo g_{10} (x) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (x) + lo g_{10} (7.2) + lo g_{10} (1 0^{- 4}))

Apply log rule:

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

lo g_{10} (1 0^{- 4}) = - 4 lo g_{10} (10)

= - (lo g_{10} (7.2) + lo g_{10} (x) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (x) + lo g_{10} (7.2) - 4)

Distribute parentheses

= - (lo g_{10} (7.2)) - (lo g_{10} (x)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (7.2) - lo g_{10} (x) + 4

- lo g_{10} (1.02 \cdot 1 0^{- 2})

\frac{1}{8} (ln (x + 4) - ln (x - 4)) + c

ln (3) + ln (7) - ln (2) - 2 ln (4)

ln (\frac{4 x ^{4} + 4 x}{x ^{2} + 2 x})

- (\frac{5}{6}) lo g_{2} (\frac{5}{6}) - (\frac{1}{6}) lo g_{2} (\frac{1}{6})

What is simplify-log_{10}(7.2x10^{-4}) ?
The solution to simplify-log_{10}(7.2x10^{-4}) is -log_{10}(7.2)-log_{10}(x)+4