Solving Exponential Equations

Pure Mathematics — Second Secondary

Substitution in exponential equations

If the equation contains powers of the same base with different exponents, such as 4x and 2x, write 4x = (22)x = (2x)2.
Then substitute y = 2x, which turns the equation into a quadratic in y.
Important since 2^x is always positive, any negative or zero value of y is rejected, because it gives no solution to the exponential equation.
If the bases cannot be made equal, such as 3^x = 10, the solution is written using logarithms, which we study in the next lesson.

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