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Chapter 10: Q69. (page 530)

If $4^{x + 2} = 48$ , then $4^{x} =$ .
$(A) 3 (B) 6.4 (C) 6.9 (D) 12 (E) 24$

Short Answer

Expert verified

The value of $4^{x} = 3$ is obtained.So,option (A) is correct.

Step by step solution

01

Step 1. Write down the given equation.

The given equation is $4^{x + 2} = 48$ .

02

Step 2. Simplify the equation.

The given equation $4^{x + 2} = 48$ is solved as:

$\begin{array}{l} 4^{x + 2} = 48.... (Given) \\ {(4)}^{x} {(4)}^{2} = 48 \\ (16) {(4)}^{x} = 48 \\ 4^{x} = 3 \end{array}$

03

Step 3. Conclusion.

Since, $4^{x} = 3$ is obtained. So, option (A) is correct.

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