SOLVING EXPONENTIAL EQUATIONS - Problem 6

To solve an exponential equation, take the log of both sides, and solve for the variable.

Problem 6: Solve for x in the equation

Solution:

Step 1: Graph the function

Note that the graph crosses the x-axis at the origin. This means that there is only one real solution and that solution is 0.

Step 2: Divide by sides of the original equation by 5:

Step 3: Take the cube root of both sides of the above equation:

Step 4: Add 3 to both sides of the above equation:

Step 5: Divide both sides of the above equation by 8:

Step 6: Take the natural logs of both sides of the above equation:

Step 7: Simplify the left side of the above equation:

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