Solving Exponential Equations and Logarithms

The video tutorial explains how to solve exponential equations using logarithms. It begins with an introduction to the method of isolating the exponential part and applying logarithms to both sides of the equation. Two examples are provided: the first involves solving 3 raised to the power of x divided by 4 equals 10, and the second involves solving 2 raised to the power of negative x divided by 5 equals 61. Each example is solved step-by-step, demonstrating the use of natural logarithms and the power property of logarithms to simplify and solve for x. The solutions are verified by substituting back into the original equations.

What is the first step in solving an exponential equation using logarithms?

• Multiply both sides by the base

• Subtract the base from both sides

• Add a constant to both sides

• Isolate the exponential part

In the first example, what logarithm is used to solve the equation?

• Common log

• Binary log

• Decimal log

• Natural log

What property of logarithms is applied to move the exponent to the front?

• Quotient property

• Change of base property

• Product property

• Power property

After solving for x in the first example, what is the approximate value of x?

• 9.5678

• 8.3836

• 10.2345

• 7.1234

Why is it important to check the solution after solving an exponential equation?

• To ensure the equation is balanced

• To verify the solution is correct

• To find the exact value of x

• To simplify the equation further

In the second example, what is the base of the exponential equation?

• 5

• 2

• 4

• 3

What is the purpose of multiplying both sides by -5 in the second example?

• To eliminate the logarithm

• To isolate the variable

• To make x positive

• To simplify the equation

What is the approximate value of x in the second example after solving?

• -30.5678

• -29.6537

• -31.2345

• -28.1234

What should be done after finding the approximate value of x in an exponential equation?

• Round the value to the nearest whole number

• Check the solution by substituting back into the original equation

• Divide the value by the base

• Multiply the value by the base

What is the result when substituting the approximate x value back into the second example equation?

• The result is less than 61

• The result is approximately 61

• The equation is not balanced

• The result is exactly 61