Exponent Equations: Methods for Solving with Same Base or Logarithms

This video provides three methods for solving exponential equations: Method 1: Equating Two Exponents with the Same Base Identify if the exponents in the equation have the same base. Ignore the base and create an equation with the exponents only. Solve the equation to isolate the variable. Verify the solution by substituting it back into the original equation. Method 2: Equating an Exponent and a Whole Number Isolate the exponential expression on one side and a whole number on the other. Rewrite the equation by converting the whole number to an exponent with the same base. Create an equation with the exponents only. Solve for the variable and check the solution's validity. Method 3: Using Logs for Terms without the Same Base Isolate the exponential expression on one side of the equation. Rewrite the equation by taking the logarithm of both sides. Rewrite the log of the exponent using logarithmic rules. Isolate the variable and solve the equation. Find the logarithmic values using a calculator. Complete the calculations, keeping in mind the order of operations. These methods provide systematic approaches to solving exponential equations, ensuring accuracy in the solutions obtained.