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

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

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expand log_{4}((sqrt(y))/((x+1)^2))

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

5 ln (x) + 2 ln (y) - 3 ln (z)

lo g_{10} (\frac{y}{z ^{5}})

lo g_{10} (\frac{4 x}{3})

lo g_{6} (x^{2} - 36) - lo g_{6} (x - 6)

lo g_{6} (\frac{x ^{6} z}{y ^{6}})

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