So, \( \log_2(8x) = 5 \).

["# Solve ( \log_2(8x) = 5 ): A Step-by-Step Guide for Beginners", "Mathematics often involves understanding logarithmic equations, and one commonly encountered problem is solving ( \log_2(8x) = 5 ). Whether you're a high school student, a college beginner, or someone refreshing their math skills, this article explains how to solve logarithmic equations clearly and effectively.", "## What is ( \log_2(8x) = 5 )?", "The expression ( \log_2(8x) ) means "to what power must 2 be raised to get ( 8x )?" In equation form:", "[\n\log_2(8x) = 5 \quad \ ext{means} \quad 2^5 = 8x\n]", "### Step 1: Convert the logarithmic equation to exponential form\nRecall the fundamental logarithmic identity:\n[\n\log_b(a) = c \quad \Leftrightarrow \quad b^c = a\n]\nApplying this identity:", "[\n2^5 = 8x\n]", "## Step 2: Simplify and solve for ( x )", "We know:", "[\n2^5 = 32\n]", "So:", "[\n32 = 8x\n]", "Now divide both sides by 8:", "[\nx = \frac{32}{8} = 4\n]", "## Final Answer", "[\n\boxed{x = 4}\n]", "## Why This Problem Matters", "Understanding ( \log_2(8x) = 5 ) builds crucial skills in:", "- Manipulating logarithmic expressions\n- Converting between logarithmic and exponential forms\n- Solving real-world problems involving growth, doubling, or scaling (like ( 2^5 = 32 ) representing 32 times a starting quantity)", "### Want to Master More Logarithmic Concepts?", "Keep practicing with related problems:", "- Solve ( \log_3(x) + \log_3(9) = 4 )\n- Evaluate ( \log_5(125x^2) = 3 )\n- Simplify ( \log_2\left(\frac{16x^3}{2}\right) )", "Using online tools or math apps can also help visualize logarithmic growth and defenses closed-form solutions.", "---", "Keywords:\nlog base 2 logarithm equation, solve ( \log_2(8x) = 5 ), logarithmic equation solved step-by-step, exponential conversion logarithms, solve ( \log_2(8x) = 5 ), math explanation logarithms, logarithmic equations for beginners."]