Solving Exponential Equations

Algebra 2 · Axiom Academy

LESSON Solving Exponential Equations Three ways to crack b^ x =a : match the base, take a log, or read the graph. When both sides can be written as powers of the same base , the equation forces the exponents to match. Rewrite, line up the bases, and read off the exponent — the fastest route when it's available. Equal bases force equal exponents Step 1 — rewrite 8 as a power of 2 Step 2 — same base, so set the exponents equal When you can't force a common base, take the logarithm of both sides. The power rule then pulls the exponent down out front, where it becomes an ordinary coefficient you can divide away. A logarithm undoes the exponent Worked example: solve 3^ x =15 Step 1 — take the log of both sides Step 2 — power rule brings the exponent down Some exponential equations mix a power with a polynomial and can't be solved exactly. Graph each side as its own function — the x-coordinate where the curves cross is the solution. The crossing point solves the equation Worked example: solve 2^ x =x+3 Step 1 — split into two functions and graph both Step 2 — read the x-value where the graphs intersect Slide across until the exponential meets the line — the gap between them closes to zero exactly at the solution. Different equations call for different tools. The form of the equation tells you which method will be cleanest — watch each example route itself to its method. Use when both sides can share a base. Use when the bases won't match, or you need a decimal.

This is the written version of the interactive lesson above. See the full Algebra 2 course.