How to solve an expression with variables in the exponents?

Accepted Solution

Answer:   use logarithmsStep-by-step explanation:Taking the logarithm of an expression with a variable in the exponent makes the exponent become a coefficient of the logarithm of the base.__You will note that this approach works well enough for ...   a^(x+3) = b^(x-6) . . . . . . . . . . . variables in the exponents   (x+3)log(a) = (x-6)log(b) . . . . . a linear equation after taking logsbut doesn't do anything to help you solve ...   x +3 = b^(x -6)There is no algebraic way to solve equations that are a mix of polynomial and exponential functions.__Some functions have been defined to help in certain situations. For example, the "product log" function (or its inverse) can be used to solve a certain class of equations with variables in the exponent. However, these functions and their use are not normally studied in algebra courses.In any event, I find a graphing calculator to be an extremely useful tool for solving exponential equations.