stion
he value of $x$ which satisfies the following equation.
\[
\log _{2}(x-1)+\log _{2}(x+5)=4
\]
ot include " $x=$ " in your answer. If there are is more than one answer, list them separated by commas.
ide your answer below:
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Step 1 ：Combine the two logarithms on the left side of the equation using the property of logarithms that states that the sum of two logarithms with the same base is the logarithm of the product of the numbers: \(\log _{2}[(x-1)(x+5)]=4\)

Step 2 ：Convert the logarithmic equation into an exponential equation using the property of logarithms that states that a logarithm of a number to a certain base is equal to another number if and only if the base raised to the second number is equal to the first number: \(2^4 = (x-1)(x+5)\)

Step 3 ：Solve this equation for x to get the solutions: \(x = -7\) and \(x = 3\)

Step 4 ：Check these solutions in the original equation because the logarithm is not defined for negative numbers and zero. When we substitute \(x = -7\) into the original equation, we get \(\log_2(-7 - 1) + \log_2(-7 + 5)\), which is not defined because the logarithm is not defined for negative numbers. Therefore, \(x = -7\) is not a solution to the equation. When we substitute \(x = 3\) into the original equation, we get \(\log_2(3 - 1) + \log_2(3 + 5)\), which is defined. Therefore, \(x = 3\) is a solution to the equation.

Step 5 ：The final answer is \(\boxed{3}\)