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algol [13]
3 years ago
12

Solve the equation of e^x-2=(1/e^6)^x+3.

Mathematics
1 answer:
Aliun [14]3 years ago
5 0

Answer:

x = -16/7

Step-by-step explanation:

The equation as written reduces to finding the solution to a 7th-degree polynomial. The one real solution, found using a graphing calculator, is ...

x ≈ 1.60945071137

_____

Since this is beyond the scope of most algebra courses, we suspect you want the solution to ...

e^(x-2) = (1/e^6)^(x+3)

x -2 = -6(x +3) . . . . . . . . take the natural log of both sides

x -2 = -6x -18 . . . . . . . . . eliminate parentheses

7x -2 = -18 . . . . . . . . . . . add 6x

7x = -16 . . . . . . . . . . . . . add 2

x = -16/7

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The instruction to "use a common denominator to divide" may be counter-intuitive to someone taught to "invert and multiply."

To find the number of glasses, we divide the amount of juice by the glass size. The divisor is the glass size, and we want to have a common divisor with the juice quantity.

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