If \( \log_2(x) + \log_2(8) = 5 \), what is the value of \( x \)?

["Solving the Equation: If ( \log_2(x) + \log_2(8) = 5 ), What is the Value of ( x )?", "Understanding logarithmic equations can seem challenging at first, but with a few key properties and simple steps, you can solve them quickly and confidently. Today, we’ll explore the equation ( \log_2(x) + \log_2(8) = 5 ) and find the exact value of ( x ).", "---", "### Understanding the Equation", "The equation combines two logarithmic terms with the same base—base 2. Recall one of the fundamental logarithmic properties:", "[\n\log_b(a) + \log_b(c) = \log_b(a \cdot c)\n]", "Using this property, we can combine the left-hand side:", "[\n\log_2(x) + \log_2(8) = \log_2(8x)\n]", "So the equation becomes:", "[\n\log_2(8x) = 5\n]", "---", "### Solving for ( x )", "Now we convert the logarithmic equation into its exponential form. The general rule is:", "[\n\log_b(A) = C \quad \ ext{is equivalent to} \quad A = b^C\n]", "Applying this rule:", "[\n8x = 2^5\n]", "Calculate ( 2^5 ):", "[\n2^5 = 32\n]", "Now solve for ( x ):", "[\n8x = 32\n]", "[\nx = \frac{32}{8} = 4\n]", "---", "### Final Answer", "The solution to the equation ( \log_2(x) + \log_2(8) = 5 ) is:", "[\n\boxed{4}\n]", "---", "### Quick Recap", "- Combine logs using ( \log_b(a) + \log_b(c) = \log_b(ac) )\n- Rewrite the equation: ( \log_2(8x) = 5 )\n- Convert to exponential form: ( 8x = 2^5 )\n- Solve: ( x = \frac{32}{8} = 4 )", "Mastering these steps helps you tackle more complex logarithmic equations with ease!", "Keywords: logarithmic equation, solve ( \log_2(x) + \log_2(8) = 5 ), ( x = 4 ), logarithmic properties, math tutorial, step-by-step solution."]