Problem 98 - College Algebra Essentials

Question

Evaluate or simplify each expression without using a calculator. $$e^{\ln 7 x^{2}}$$

Step-by-Step Solution

Answer

The simplified result of the mathematical expression \(e^{\ln 7x^{2}}\) is \(7x^{2}\).

Step 1: Identify the Expression

We evaluate or simplify:
Evaluate or simplify each expression without using a calculator.
$$e^{\ln 7 x^{2}}$$

Step 2: Apply Logarithm Properties

Key properties: \(\log_a(a^x) = x\), \(\log_a(1) = 0\), \(e^{\ln x} = x\), \(\ln(e^x) = x\).

Step 3: Result

The simplified result of the mathematical expression \(e^{\ln 7x^{2}}\) is \(7x^{2}\).