X=? a^2x × a^x = a^4x?

Vastaus:

To solve the equation ( a^{2x} times a^x = a^{4x} ), we can use the properties of exponents.

1. Recall that when multiplying two expressions with the same base, you add the exponents. Thus, we can simplify the left side:

[
a^{2x} times a^x = a^{2x + x} = a^{3x}
]

2. Now, we set this equal to the right side of the equation:

[
a^{3x} = a^{4x}
]

3. Since the bases are the same (assuming ( a neq 0 ) and ( a neq 1 )), we can equate the exponents:

[
3x = 4x
]

4. To solve for ( x ), subtract ( 3x ) from both sides:

[
0 = 4x - 3x
]
[
0 = x
]

Thus, the solution is:

[
boxed{0}
]


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