Equations » Power equations

A power formula is always of the form y = axb.
A power equation is always of the form axb = c.

One or two solutions?

A power equation always has one solution when you have an odd exponent.
A power equation has two, one or zero solutions when you have an even exponent.
Think of a quadratic equation (even exponent):
x2 = 4 has two solutions, namely x = –2 or x = 2.
x2 = 0 has one solution, namely x = 0.
x2 = –1 has no solutions.

Root = power

Every root can be written as a power.
The rule is n-th root of x = x1/n.

Example 1
 3x4 + 8 = 1883
 3x4 = 1875
 x4 = 625
 x = –forth root of 625 of x = forth root of 625
 x = –5 or x = 5

Example 2
 500 – 2x5 = 14
 2x5 = 486
 x5 = 243
 x = fifth root of 243 = 3

Example 3
 7x3 + 6 = –204
 7x3 = –210
 x3 = –30
 x = third root of minus 30 ≈ –3.107

Example 4

On the graph of y = 112x0.43 lies point (x; 14.5).
Calculate x. Round to 4 decimals.

Answer:

14.5 = 112x0.43
x0.43 = 14.5112
x = bracket open14.5112bracket close1/0.43 ≈ 0.0086