Test Index

Indices

© examsnet.com

Question : 21 of 86

Marks: +1, -0

The value of

x

2^{x+4}-2^{x+2}=3

0
$-2$
2
$-1 .$

Solution:

Concept:

Factor out a common exponential term to isolate

x

.

Explanation:

Write

2^{x+4}

as

2^2 \cdot 2^{x+2} = 4 \cdot 2^{x+2}

.

Then the equation becomes

4 \cdot 2^{x+2} - 2^{x+2} = 3

.

Factor out

2^{x+2}

:

(4 - 1) \cdot 2^{x+2} = 3

.

So

3 \cdot 2^{x+2} = 3

.

Divide both sides by

3

:

2^{x+2} = 1

.

Since

1 = 2^0

, we have

2^{x+2} = 2^0

.

Thus

x+2 = 0

, so

x = -2

.

Answer:

x = -2

© examsnet.com

Go to Question:

Prev Question

Next Question