Question
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Answer
\( y = 0.5 \)
Solution
Solve the equation \( 7^{4y}=49 \).
Solve the equation by following steps:
- step0: Solve for \(y\):
\(7^{4y}=49\)
- step1: Rewrite in exponential form:
\(7^{4y}=7^{2}\)
- step2: Set the exponents equal:
\(4y=2\)
- step3: Divide both sides:
\(\frac{4y}{4}=\frac{2}{4}\)
- step4: Divide the numbers:
\(y=\frac{1}{2}\)
The solution to the equation \(7^{4y}=49\) is \(y=\frac{1}{2}\) or \(y=0.5\).
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Simplify this solution Bonus Knowledge
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!
