Question

B%204%20log_%7B2%7D%28x%29%20" id="TexFormula1" title=" log_{2}(2x + 1) - 5 log_{4}( {x}^{2} ) + 4 log_{2}(x) " alt=" log_{2}(2x + 1) - 5 log_{4}( {x}^{2} ) + 4 log_{2}(x) " align="absmiddle" class="latex-formula">

Answer 1

Evaluate each expression individually and then combine like terms:

5 log₄(x²) = 5$\frac{log (x^{2}) }{log (4) }$ = 5$\frac{log (x^{2}) }{log (2^{2}) }$ = 5$\frac{2 log (x) }{2 log (2) }$ = 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$\frac{(2x+1)x^{4} }{x^{5}}$

= log₂$\frac{2x+1 }{x}$