Question

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How would I solve for x in this equation to the nearest thousandth?

22^3x+2=144

Answer 1

(22^3)x + 2 = 144

10648x + 2 = 144

10648x = 142

x = 142/10648

x = 0.01333583...

Nearest thousandth,

x = 0.013

Answer 2

x ≈ -0.131

Explanation:

To solve the equation for "x", 22^(3x+2) = 144 , you can use the "log" function on your calculator with this equation:

`exponent = (log(answer))/(log(base))`

Before you use "log", make sure you have only the exponent and its base on one side, and a number on the other side.

Identify the parts in 22^(3x+2) = 144.

exponent - 3x+2

answer - 144

base - 22

First, focus on isolating the exponent using "log". Then, isolate "x" as you normally would using reverse operations.

22^(3x+2) = 144

3x + 2 =
`(log(144))/(log(22))` Use "log"

3x + 2 = 1.60781140168 Isolate "x"

3x = 1.60781140168 - 2 Subtract 2 from both sides

3x = -0.39218859832 Divide both sides by 3

x = -0.13072953277 Round to nearest thousandth (3 decimals)

x ≈ -0.131