Each of the expressions below represents a function of x , for a > 0 . Assign to each a simplified expression whieh is equivalent for all x > 0 . =0ln((e^(x ln(2)))/(2))quad=0e^(ln(x)+ln(3))quad3ln(x+3) :.ln((3^(x)6^(2x))/(2^(4x)))quad=0ln((e^(x)e^(3))^(2)) 3a 2(x+3) (x+3)^(2) x ln(27//4) (x-1)ln(2)

<p> <br />1. Using the logarithmic property \( \ln(e^{a}) = a \), the expression \( \ln(e^{x\ln(2)/2}) \) simplifies to \( x\ln(2)/2 \), which matches with Option E. \( (x-1) \ln (2) \).<br />2. The expression \( uQ^{\ln(x)}+\ln(3) \) is not recognized.<br />3. Using the properties \( e^{\ln(a)} = a \) and \( e^{a\ln(b)} = b^{a} \), the expression \( 30e^{2\ln(x+3)} \) simplifies to \( 30(x+3)^{2} \), which matches with Option C. \( (x+3)^{2} \).<br />4. The symbol "อ" in the expression \( อ \ln(3^{x}6^{2x}/2^{4x}) \) is not recognized.<br />5. The symbol "อ" in the expression \( อ \ln((e^{x}e^{3})^{2}) \) is not recognized.<br /></p>