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Chapter 3: Problem 3

Determine whether each \(x\) -value is a solution (or an approximate solution) of the equation. \(4^{2 x-7}=64\) (a) \(x=5\) (b) \(x=2\)

Short Answer

Expert verified
For the equation \(4^{2x-7}=64\), the solution is x=5 and not x=2.

Step by step solution

01

Simplify the equation

First step is to simplify the equation by expressing 64 as a power of 4. As we know \(4^3=64\), thus the equation can be rewritten as: \(4^{2x-7}=4^3\).
02

Substitute x-value 5

For part (a), plug in x=5 into the simplified equation. It becomes: \(4^{2*5-7}=4^3\), which simplifies to: \(4^{3}=4^3\). Since both sides are equal, x=5 is a solution of the equation.
03

Substitute x-value 2

For part (b), plug in x=2 into the simplified equation. It becomes: \(4^{2*2-7}=4^3\), which simplifies to: \(4^{-3}=4^3\). Since both sides are not equal, x=2 is not a solution of the equation.

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