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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

lo g_{3} (z^{5} x)

lo g_{3} (\frac{4 ( x - 5 ) ^{2}}{x ^{4} ( x - 1 ) ^{3}})

ln (n) - ln (n + 1)

lo g_{6} (b) + 2 lo g_{6} (c) + \frac{lo g _{6} ( a )}{2}

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