Solving Exponential Equations with Logarithms

In this lesson, we will learn how to solve more challenging exponential equations. While working with exponential equations, we often encounter a straightforward case where finding a solution does not require the use of logarithms. This favorable situation arises when both sides of the equation have the same base or can easily be converted into the same base. However, there are instances where we cannot express each side of the equation using the same base, leading us to the harder case. When faced with this more complex scenario, we turn to logarithms and utilize the power property to attain a solution. To tackle exponential equations with different bases, we apply the following steps: Identify that the equation cannot be simplified by expressing both sides with the same base. Choose an appropriate base for logarithms (common choices include base 10 and base e, also known as the natural logarithm). Take the logarithm of both sides of the equation, using the chosen base. Utilize the power property of logarithms to simplify the equation. Solve the resulting equation for the unknown variable. Check the obtained solution by substituting it back into the original equation to ensure its validity.