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题目

解题步骤

1. Understand the question

   solve the exponential equation $\\sqrt{a} \\cdot \\sqrt{a} \\cdot a^3 = a^x$ for x.
   options:
   x equals 3
   x equals 2
   x equals $\\frac{2}{3}$
   x equals 4

2. Explanation

   Step1: Rewrite root as exponent

   $\sqrt{a} = a^\frac{1}{2}$

   Step2: Substitute into left-hand side

   $a^\frac{1}{2} \cdot a^\frac{1}{2} \cdot a^3$

   Step3: Add exponents (same base)

   $\frac{1}{2} + \frac{1}{2} + 3 = 4$

   Step4: Equate exponents (same base)

   $a^4 = a^x \implies x=4$

3. Final answer

   x equals 4

答案

Question Analysis

OCR Text

solve the exponential equation $\\sqrt{a} \\cdot \\sqrt{a} \\cdot a^3 = a^x$ for x.
options:
x equals 3
x equals 2
x equals $\\frac{2}{3}$
x equals 4

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