Question

Using a table of values, determine the solution to the equation below to the nearest fourth of a unit. 2^x=1-3^x

Answer 1

Answer:

Option (1)

Step-by-step explanation:

Given equation is,

$2^x=1-3^x$

To determine the solution of the equation we will substitute the values of 'x' given in the options,

Option (1)

For x = -0.75

$2^{-0.75}=1-3^{-0.75}$

0.59 = 1 - 0.44

0.59 = 0.56

Since, values on both the sides are approximately same.

Therefore, x = -0.75 will be the answer.

Option (2)

For x = -1.25

$2^{-1.25}=1-3^{-1.25}$

0.42 = 1 - 0.25

0.42 = 0.75

Which is not true.

Therefore, x = -1.25 is not the answer.

Option (3)

For x = 0.75

$2^{0.75}=1-3^{0.75}$

1.68 = 1 - 2.28

1.68 = -1.28

Which is not true.

Therefore, x = 0.75 is not the answer.

Option (4)

For x = 1.25

$2^{1.25}=1-3^{1.25}$

2.38 = 1 - 3.95

2.38 = -2.95

It's not true.

Therefore, x = 1.25 is not the answer.