If 5^{x-3}=8, then what is x equal to?
- A. \frac{3}{1-\log_{10} 2} ✓
- B. \frac{3}{1+\log_{10} 2}
- C. \frac{2}{1-\log_{10} 2}
- D. \frac{5}{1-\log_{10} 2}
Correct Answer: A. \frac{3}{1-\log_{10} 2}
Explanation
Taking \log_{10} on both sides gives (x-3)\log_{10} 5 = \log_{10} 8 = 3\log_{10} 2. Substitute \log_{10} 5 = 1 - \log_{10} 2 to get x-3 = \frac{3\log_{10} 2}{1-\log_{10} 2}. Then x = 3 + \frac{3\log_{10} 2}{1-\log_{10} 2} = \frac{3 - 3\log_{10} 2 + 3\log_{10} 2}{1-\log_{10} 2} = \frac{3}{1-\log_{10} 2}.
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