(3) \( 7^{4 y}=49 \)

To solve the equation \( 7^{4y} = 49 \), first notice that \( 49 \) can be rewritten as \( 7^2 \). This gives us the equation \( 7^{4y} = 7^2 \). Since the bases are the same, we can set the exponents equal to each other: \( 4y = 2 \). Now, divide both sides by 4, yielding \( y = \frac{2}{4} = \frac{1}{2} \). Thus, the solution is \( y = \frac{1}{2} \). If you’re ever unsure about exponential equations, try converting to the same base or using logarithms! A common mistake is forgetting to simplify constants like \( 49 \) to their base forms, which can lead to complicated or incorrect solutions. Keep it simple, and you’ll avoid such pitfalls!