The value of x in the equation [tex]64^{3x} = 512^{2x}[/tex] is infinite
How to determine the value of x?
The equation is given as:
[tex]64^{3x} = 512^{2x}[/tex]
Rewrite [tex]64^{3x}[/tex] and [tex]512^{2x}[/tex] in base 2
[tex]2^{6*3x} = 2^{9*2x}[/tex]
Evaluate 6 * 3x and 9 * 2x
[tex]2^{18x} = 2^{18x}[/tex]
By comparing the exponents, we have:
18x = 18x
Divide both sides by 18x
1 = 1
Hence, the value of x in the equation is infinite
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