What is log_{10}(2x-4)-0.5log_{10}(x) ?

The solution to log_{10}(2x-4)-0.5log_{10}(x) is log_{10}((2x-4)/(x^{0.5)})

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simplify log_{10}(2x-4)-0.5log_{10}(x)

simplify

lo g_{10} (2 x - 4) - 0.5 lo g_{10} (x)

lo g_{10} (\frac{2 x - 4}{x ^{0.5}})

Solution steps

lo g_{10} (2 x - 4) - 0.5 lo g_{10} (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

0.5 lo g_{10} (x) = lo g_{10} (x^{0.5})

= lo g_{10} (2 x - 4) - lo g_{10} (x^{0.5})

Apply log rule:

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

lo g_{10} (2 x - 4) - lo g_{10} (x^{0.5}) = lo g_{10} (\frac{2 x - 4}{x ^{0.5}})

= lo g_{10} (\frac{2 x - 4}{x ^{0.5}})

ln (\frac{2 ^{0.538 + 1} - 1}{( 0.538 - 1 ) x})

\frac{ln ( x ) - ln ( 4 )}{x - 4}

2 ln (a) - 4 ln (y)

\frac{1}{x ^{2}} + ln^{2} (x) + 2 ln (x)

ln (\frac{x}{y}) - ln (z)

What is log_{10}(2x-4)-0.5log_{10}(x) ?
The solution to log_{10}(2x-4)-0.5log_{10}(x) is log_{10}((2x-4)/(x^{0.5)})