2^x-4x=0 find the value of x in the equation

9514 1404 393

  x ≈ 0.309906932381 or 4

Step-by-step explanation:

There are no algebraic methods of solving a mixed exponential and polynomial equation. The value of x can be found by guessing, or by other means such as trial and error or graphing.

Attached is a graph showing two solutions. x = 4 is the integer solution (2^4 = 4·4). The irrational solution is approximately x ≈ 0.309906932381. That precision is obtained by Newton's method iteration, easily done by a graphing calculator.

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

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step-by-step explanation: