What is expand log_{10}(4/(5x)) ?

The solution to expand log_{10}(4/(5x)) is 2log_{10}(2)-log_{10}(5)-log_{10}(x)

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expand log_{10}(4/(5x))

expand

lo g_{10} (\frac{4}{5 x})

2 lo g_{10} (2) - lo g_{10} (5) - lo g_{10} (x)

Solution steps

lo g_{10} (\frac{4}{5 x})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{10} (4) = 2 lo g_{10} (2)

= 2 lo g_{10} (2) - (lo g_{10} (x) + lo g_{10} (5))

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

= 2 lo g_{10} (2) - lo g_{10} (5) - lo g_{10} (x)

3 ln (2) + 2 ln (x) - \frac{1}{2} ln (x - 4)

ln (\frac{p}{( 1 - p )})

2 ln (x) + ln (y) - 4 x - y

\frac{4}{3} ln ∣ x - 1 ∣ - \frac{1}{3} ln ∣ x - 4 ∣

\frac{1}{2} lo g_{b} (3) + 3 lo g_{b} (13) - 3 lo g_{b} (2)

What is expand log_{10}(4/(5x)) ?
The solution to expand log_{10}(4/(5x)) is 2log_{10}(2)-log_{10}(5)-log_{10}(x)