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

["# Solving (\log_2(x) + \log_2(8) = 5): Step-by-Step Guide", "If you're tackling logarithmic equations like (\log_2(x) + \log_2(8) = 5), knowing how to simplify and solve them correctly can boost your math confidence. Many students wonder: What is the value of (x) in this equation? In this easy-to-follow guide, we’ll solve (\log_2(x) + \log_2(8) = 5) step by step and uncover the value of (x). Plus, you’ll learn useful logarithmic rules to apply to similar problems.", "---", "## Understanding the Equation", "Start with the equation:\n[\n\log_2(x) + \log_2(8) = 5\n]", "This uses the logarithm addition rule, which states:\n[\n\log_b(a) + \log_b(c) = \log_b(a \cdot c)\n]\nApplying this here:", "[\n\log_2(x) + \log_2(8) = \log_2(8x)\n]", "So the equation becomes:\n[\n\log_2(8x) = 5\n]", "---", "## Eliminate the Logarithm", "To solve for (x), remove the logarithm by rewriting the equation in exponential form:\n[\n8x = 2^5\n]", "Calculate (2^5):\n[\n2^5 = 32\n]", "Now:\n[\n8x = 32\n]", "---", "## Solve for (x)", "Divide both sides by 8:\n[\nx = \frac{32}{8} = 4\n]", "---", "## Check the Solution (Optional but Recommended)", "Always verify your answer by plugging (x = 4) back into the original equation:\n[\n\log_2(4) + \log_2(8) = ?\n]", "Calculate each term:\n[\n\log_2(4) = 2 \quad \ ext{since } 2^2 = 4\n\log_2(8) = 3 \quad \ ext{since } 2^3 = 8\n]", "Add them:\n[\n2 + 3 = 5\n]", "Since it matches the right-hand side, (x = 4) is indeed the correct solution.", "---", "## Why This Approach Works", "This method uses key logarithmic properties:\n1. Sum to product rule: Combining logs into a single logarithm.\n2. Exponentiation: Reverting from (\log_b(y) = z) to (y = b^z).\nThese tools are fundamental in solving logarithmic equations efficiently and accurately.", "---", "## Conclusion", "The value of (x) satisfying (\log_2(x) + \log_2(8) = 5) is\n[\n\boxed{4}\n]\nUnderstanding each step helps not only solve this problem but also prepares you for more complex equations involving logarithms. Keep practicing, and math will become even clearer!", "---", "### Related Keywords for SEO:\nlog base 2 logarithm equation, solve logarithmic equation, value of x in log equation, logarithmic identity calculation, step-by-step logarithm solution, simplify log expressions, exponential form logarithm, math problem solving, logarithms high school tutorial, reduce log sum to product, logarithmic equation explained.", "Meta Title:\nSolve (\log_2(x) + \log_2(8) = 5): Correct Value of (x) Explained\nMeta Description:\nLearn step-by-step how to solve (\log_2(x) + \log_2(8) = 5) for (x = 4), using logarithmic rules and verification. Free math tutorial.", "---", "If you found this guide helpful, share it and subscribe for more clear math tutorials on logging, algebra, and problem-solving strategies!"]