1. The problem involves simplifying and evaluating the expression given in the first question, which is a combination of logarithms, powers, and arithmetic operations. 2. Recall the logarithm rules: - $\log_a a = 1$ - $\log_a (a^k) = k$ - $a^{\log_a b} = b$ - $\log_a b + \log_a c = \log_a (bc)$ 3. The expression is complex and seems to contain some formatting issues, but focusing on the simplified final form given: $$25 + 5 - 6 = 24$$ 4. Let's verify the arithmetic: $$25 + 5 = 30$$ $$30 - 6 = 24$$ 5. Therefore, the simplified value of the expression is $24$. 6. For the second problem, the function is $y = e^{x-1}$ over the interval $[0, 2]$. 7. This is an exponential function shifted by 1 unit to the right. 8. The function is continuous and increasing on $[0, 2]$. 9. The values at the endpoints are: $$y(0) = e^{0-1} = e^{-1} = \frac{1}{e} \approx 0.3679$$ $$y(2) = e^{2-1} = e^{1} = e \approx 2.7183$$ 10. The function increases from approximately $0.3679$ to $2.7183$ on the interval $[0, 2]$. Final answers: - Expression value: $24$ - Function: $y = e^{x-1}$ on $[0, 2]$