Using a table of values, determine the solution to the equation below to the nearest fourth of a unit. 2x-4=3 to the negative x power+1
Answers
Solution :-
→ 2x - 4 = 3^(-x) + 1
solving LHS, by putting all given values from options,
→ f(1) = 2 * 1 - 4 = 2 - 4 = (-2)
→ f(3.25) = 2(3.25) - 4 = 6.5 - 4 = 2.5
→ f(2.5) = 2(2.5) - 4 = 5 - 4 = 1
→ f(2) = 2(2) - 4 = 4 - 4 = 0 .
similarly, putting all given values from options in RHS,
→ f(1) = 3^(-1) + 1 = (1/3) + 1 = (4/3) = 1.3334
→ f(3.25) = 3^(-3.25) + 1 = 0.0281 + 1 = 1.0281
→ f(2.5) = 3^(-2.5) + 1 = 0.0642 + 1 = 1.0642
→ f(2) = 3^(-2) + 1 = (1/3²) + 1 = (1/9) + 1 = (10/9) = 1.1111
now, comparing wr get,
- (-2) is not close to 1.3334 .
- 2.5 is not close to 1.0281 .
- 1 is close to 1.0642 .
- 0 is not close to 1.1111 .
therefore, we can conclude that, the solution to the equation is x ≈ 2.5 (C) .
Learn more :-
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