Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 12, 2024

Find the value of $x$ in the equation $y^{12} = y^{2x}$ .

STEP 1

Assumptions
1. The equation is $y^{12} = y^{2x}$ .
2. The variable $y$ is not equal to 0 or 1, as these would make the equation trivial (any value of $x$ would satisfy the equation if $y=1$ , and the equation would not hold for any $x$ if $y=0$ ).
3. We are looking for the value of $x$ .

STEP 2

We can solve the equation by setting the exponents equal to each other, since the bases are the same and $y$ is not 0 or 1.
$y^{12} = y^{2x} \Rightarrow 12 = 2x$

STEP 3

Now, we can solve for $x$ by dividing both sides of the equation by 2.
$\frac{12}{2} = \frac{2x}{2}$

STEP 4

Calculate the value of $x$ .
$x = \frac{12}{2} = 6$
The value of $x$ in the equation $y^{12} = y^{2x}$ is 6.

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