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Table I x 0.792 ◻ 1.5 1.661 f(x)=b^(x) 3 7 8 10

Table I\newline\begin{tabular}{lrrrr}\newlinex x & 00.792792 & □ \square & 11.55 & 11.661661 \\\newline\hlinef(x)=bx f(x)=b^{x} & 33 & 77 & 88 & 1010\newline\end{tabular}

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Full solution

Q. Table I\newline\begin{tabular}{lrrrr}\newlinex x & 00.792792 & □ \square & 11.55 & 11.661661 \\\newline\hlinef(x)=bx f(x)=b^{x} & 33 & 77 & 88 & 1010\newline\end{tabular}
  1. Solve for b: We have f(0.792)=3f(0.792) = 3, which means b0.792=3b^{0.792} = 3. Let's solve for b.\newlineTake the logarithm of both sides to get 0.792⋅log⁡(b)=log⁡(3)0.792 \cdot \log(b) = \log(3).
  2. Isolate log⁡(b)\log(b): Divide both sides by 0.7920.792 to isolate log⁡(b)\log(b). So, log⁡(b)=log⁡(3)0.792\log(b) = \frac{\log(3)}{0.792}.
  3. Calculate log⁡(b)\log(b): Use a calculator to find log⁡(3)\log(3) and then divide by 0.7920.792. log⁡(3)≈0.4771\log(3) \approx 0.4771, so log⁡(b)≈0.47710.792\log(b) \approx \frac{0.4771}{0.792}.
  4. Find bb: Calculate log⁡(b)≈0.47710.792\log(b) \approx \frac{0.4771}{0.792} to get log⁡(b)≈0.6024\log(b) \approx 0.6024.
  5. Use exponentiation: Now, to find bb, we need to use the inverse of the logarithm, which is the exponentiation. So, b=10log⁡(b)=100.6024.b = 10^{\log(b)} = 10^{0.6024}.
  6. Final calculation: Use a calculator to find 100.602410^{0.6024}. b≈100.6024≈4.02b \approx 10^{0.6024} \approx 4.02.

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