What is simplify-log_{10}(5x10^{-4}) ?

The solution to simplify-log_{10}(5x10^{-4}) is -log_{10}(5)-log_{10}(x)+4

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simplify-log_{10}(5x10^{-4})

simplify

- lo g_{10} (5 x 1 0^{- 4})

- lo g_{10} (5) - lo g_{10} (x) + 4

Solution steps

- lo g_{10} (5 x \cdot 1 0^{- 4})

Apply log rule:

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

lo g_{10} (5 x \cdot 1 0^{- 4}) = lo g_{10} (5) + lo g_{10} (x) + lo g_{10} (1 0^{- 4})

= - (lo g_{10} (x) + lo g_{10} (5) + 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} (5) + lo g_{10} (x) - 4 lo g_{10} (10))

4 lo g_{10} (10) = 4

= - (lo g_{10} (x) + lo g_{10} (5) - 4)

Distribute parentheses

= - (lo g_{10} (5)) - (lo g_{10} (x)) - (- 4)

Apply minus-plus rules

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

= - lo g_{10} (5) - lo g_{10} (x) + 4

3 ln (x) - ln (x + 6) - ln (x - 6)

ln (\frac{R}{0.203})

5 ln (x) + 2 ln (y) + ln (z)

ln (\frac{100}{10})

lo g_{4} (\frac{3 x ^{2}}{y ^{3}})

What is simplify-log_{10}(5x10^{-4}) ?
The solution to simplify-log_{10}(5x10^{-4}) is -log_{10}(5)-log_{10}(x)+4