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Chapter 4: Problem 121

Explain how to solve an exponential equation when both sides can be written as a power of the same base.

Short Answer

Expert verified
To solve an exponential equation with both sides expressed as powers of the same base, the solution involves identifying the common base, equating the exponents, and then solving the resulting equation.

Step by step solution

01

Identify the common base

Firstly, it is essential to identify a common base for both sides of the equation. In many cases, this involves factoring or simplifying the equation.
02

Equate the exponents

Once both sides of the equation have been expressed as a power of the same base, the next step is to set the exponents of the two sides equal to each other. This is justified by the fact that if \(a^b = a^c\) with \(a>0\) and \(a鈮�1\), then \(b=c\). This results in a simpler equation to solve.
03

Solve the equation

The equation from Step 2 can be solved using standard algebraic techniques. Depending on the complexity of the exponent equations, you may need to use techniques such as the distributive property or factoring.

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