Questions: What is the value of x in the equation y^12 = y^(2x)?

What is the value of x in the equation y^12 = y^(2x)?
Transcript text: What is the value of $x$ in the equation $y^{12}=y^{2 x}$ ?
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Solution

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Solution Steps

Step 1: Start with the equation \(y^a = y^{bx}\).

Given that \(a = 12\) and \(b = 2\), we need to find the value of \(x\) that satisfies this equation.

Step 2: Since the bases on both sides of the equation are the same and the equation holds true, the exponents must be equal.

Therefore, we set \(a = bx\).

Step 3: Solve the resulting equation for \(x\), which gives \(x = \frac{{a}}{{b}}\).

Substituting the given values, we get \(x = \frac{12}{2}\).

Final Answer:

The value of \(x\) is \(x = 6\).

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