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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

4 lo g_{10} (x) = lo g_{10} (x^{4})

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

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

Apply log rule:

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

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

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

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