Math Equations

Exponential Equations

Solving exponential equations by taking the logs of both of the equations sides may transform the question into solving a simpler equation.

2^{(x + 2)} = 64
The log of both sides to base 2 is:
log₂(₂^{(x + 2)}) = log₂(2⁶)
Thus, x + 2 = 6
Or, x = 4

Let x = p + q
Then, x³ = p³ + q³ + 3pqx
Or, x³ – 3pqx – (p³ + q³) = 0
Thus, pq = -2 (1)
And, p³ + q³ = -7 (2)

A new method for solving cubic equations is introduced. Similar to Cardano’s method, the question is reduced into solving a quadratic equation.