Polynomial addition with exponentiation

Question

I have the following formula:

$$a \times (1+z)^p = b$$

How can I solve for $z$?

Answer 1

Very little effort is required to show that: \begin{align} (1 + z)^p &= \frac{b}{a} \\ 1 + z &= \left(\frac{b}{a}\right)^{1/p} \\ z &= \left(\frac{b}{a}\right)^{1/p} -1 \end{align}

Answer 2

This is not a polynomial equation. You need to remember enough about the laws of exponents to solve it.

$$ a(1+z)^p = b $$ implies $$ 1+z = (b/a)^{1/p} $$ so $$ z = (b/a)^{1/p} -1 \ $$