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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

- \frac{1}{2} ln (y + 1) + \frac{1}{2} ln (y - 1)

lo g_{7} (7 m n^{4})

lo g_{10} (\frac{a b ^{7}}{c ^{8}})

lo g_{2} (A B^{2})

ln (\frac{( 3 ^{x} 6 ^{2 x} )}{2 ^{2 x}})

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