X=? a^2x × a^x = a^4x?

Vastaus:

To solve the equation ( a^{2x} imes a^x = a^{4x} ), we can use the property of exponents that states when you multiply exponents with the same base, you add the exponents.

So, we can rewrite the left side of the equation:

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

Now our equation becomes:

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

Since the bases are the same (assuming ( a
eq 0 ) and ( a
eq 1 )), we can set the exponents equal to each other:

[
3x = 4x
]

Next, we can isolate ( x ) by subtracting ( 3x ) from both sides:

[
0 = 4x - 3x
]

[
0 = x
]

Thus, the solution is:

[
oxed{0}
]

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