Exponents, Logarithms and their Applications — Solving the exponential equations

About this lesson

This unit introduces exponential equations and their solution methods. It begins with a real-world context of binary fission in amoeba, where one cell divides into two, prompting questions about the number of cells after a given time and the time needed to reach a certain number of cells. The unit then defines an exponential function as an equation with a variable in the exponent, such as 2^(x+1)=8. It teaches two main solution strategies: first, when bases are equal (a^m = a^n), set exponents equal; second, when exponents are equal (a^m = b^m), consider cases for the base (zero, odd/even exponent). Worked examples and exercises involve solving equations like 2^(3x)=8, 3^(x+2)=7^(x+2), and 4^(x^2)=32^(x-4), as well as finding x for given function values like f(x)=2^(x+1)=32. The unit includes practice problems, multiple-choice questions, and an error-analysis exercise comparing two students' solutions to 2×2^x=16. By the end, students should be able to solve exponential equations using these rules and apply them to function value problems.