Evaluate each expression individually and then combine like terms:
5 log₄(x²) = 5[tex]\frac{log (x^{2}) }{log (4) }[/tex] = 5[tex]\frac{log (x^{2}) }{log (2^{2}) }[/tex] = 5[tex]\frac{2 log (x) }{2 log (2) }[/tex] = 5 log₂x = log₂x⁵
4 log₂(x) = log₂(x)⁴ = log₂(x⁴)
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log₂(2x + 1) - 5 log₄(x²) + 4 log₂(x)
= log₂(2x + 1) - log₂x⁵ + log₂(x⁴)
= log₂[(2x + 1)*(x⁴) ÷ x⁵]
= log₂[tex]\frac{(2x+1)x^{4} }{x^{5}}[/tex]
= log₂[tex]\frac{2x+1 }{x}[/tex]
