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If 42x−3 = 2^x-3, find the value of x.

May 18, 2026Mathematics

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Here are the solutions to the questions:

1. If $4^{2x-3} = 2^{x-3}$ , find the value of $x$ .

Express both sides of the equation with the same base.
Since $4 = 2^2$ , we can rewrite $4^{2x-3}$ as $(2^2)^{2x-3}$ .
$(2^2)^{2x-3} = 2^{2(2x-3)} = 2^{4x-6}$
The equation becomes:
$2^{4x-6} = 2^{x-3}$
Equate the exponents.

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