What is expand log_{10}(r/(8s)) ?

The solution to expand log_{10}(r/(8s)) is log_{10}(r)-3log_{10}(2)-log_{10}(s)

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expand log_{10}(r/(8s))

expand

lo g_{10} (\frac{r}{8 s})

lo g_{10} (r) - 3 lo g_{10} (2) - lo g_{10} (s)

Solution steps

lo g_{10} (\frac{r}{8 s})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{r}{8 s}) = lo g_{10} (r) - lo g_{10} (8 s)

= lo g_{10} (r) - lo g_{10} (8 s)

Apply log rule:

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

lo g_{10} (8 s) = lo g_{10} (8) + lo g_{10} (s)

= lo g_{10} (r) - (lo g_{10} (s) + lo g_{10} (8))

lo g_{10} (8) = 3 lo g_{10} (2)

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

- (3 lo g_{10} (2) + lo g_{10} (s)) : - 3 lo g_{10} (2) - lo g_{10} (s)

= lo g_{10} (r) - 3 lo g_{10} (2) - lo g_{10} (s)

2 lo g_{3} (x) + 3 lo g_{3} (z)

ln (\frac{( a ^{4} )}{b ^{- 2} c ^{2}})

10 lo g_{10} (\frac{1 0 ^{12} \cdot 0.5}{4 \cdot π \cdot 20 0 ^{2}})

6 ln \frac{y}{x} - 1 - ln \frac{y}{x} + 4 - 5 ln ∣ x ∣

3727.8 \cdot ln (\frac{( 23180 + 56088 )}{23180})

What is expand log_{10}(r/(8s)) ?
The solution to expand log_{10}(r/(8s)) is log_{10}(r)-3log_{10}(2)-log_{10}(s)