What is 2log_{10}(x-1)-log_{10}(4) ?

The solution to 2log_{10}(x-1)-log_{10}(4) is log_{10}(((x-1)^2)/4)

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simplify 2log_{10}(x-1)-log_{10}(4)

simplify

2 lo g_{10} (x - 1) - lo g_{10} (4)

lo g_{10} (\frac{( x - 1 ) ^{2}}{4})

Solution steps

2 lo g_{10} (x - 1) - lo g_{10} (4)

Apply log rule:

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

2 lo g_{10} (x - 1) = lo g_{10} ((x - 1)^{2})

= lo g_{10} ((x - 1)^{2}) - lo g_{10} (4)

Apply log rule:

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

lo g_{10} ((x - 1)^{2}) - lo g_{10} (4) = lo g_{10} (\frac{( x - 1 ) ^{2}}{4})

= lo g_{10} (\frac{( x - 1 ) ^{2}}{4})

5 + ln (3.6) - 2 ln (4.6)

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

ln (x + 2) - ln (2 x - 1)

ln (\frac{9}{4})

lo g_{a} (\frac{( x + y ) ^{3}}{( x - y ) ^{2}})

What is 2log_{10}(x-1)-log_{10}(4) ?
The solution to 2log_{10}(x-1)-log_{10}(4) is log_{10}(((x-1)^2)/4)