\(15 \cdot 15^{x-1} - 82 = 62 \cdot 3\)
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\(15 \cdot 15^{x-1} - 82 = 186\)
\(15 \cdot 15^{x-1} = 186 + 82\)
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\(15 \cdot 15^{x-1} = 268\)
\(15^{x-1} = \frac{268}{15}\)
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\(15^{x-1} = 17,87\)
\(\log_{15} 15^{x-1} = \log_{15} 17,87\)
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\(x-1 = \log_{15} 17,87\)
\(x-1 = \frac{\log 17,87}{\log 15} \approx 1,065\)
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\(x \approx 2,065\)
Ответ: \(x \approx 2,065\)