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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

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

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

Simplify

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

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

5 lo g_{10} (x^{3}) - 2 lo g_{10} (x^{4})

lo g_{b} (\frac{p ^{3} q ^{6}}{m ^{4} b ^{7}})

lo g_{10} (3 x + 9) + lo g_{10} (x + 8)

lo g_{b} (x) + lo g_{b} (x + 6) - lo g_{b} (24)

ln (\frac{x - 1}{x})

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