Logarithmic and Exponential Equations

This video tutorial explains how to solve an exponential equation by isolating the exponential part and applying logarithms. The process involves subtracting and dividing to isolate the exponential term, then using logarithms to solve for the variable. The tutorial provides both exact and approximate solutions, rounded to four decimal places, and verifies the solution by substituting it back into the original equation. The video concludes with a brief discussion on the slight discrepancy due to rounding.

What is the primary goal when solving an exponential equation?

• To graph the equation

• To eliminate the variable

• To determine both the exact and approximate solutions

• To find the variable's value in terms of another variable

What is the first step in isolating the exponential part of the equation?

• Multiply both sides by 100

• Divide both sides by 31

• Add 17 to both sides

• Subtract 17 from both sides

After isolating the exponential part, what operation is performed next?

• Take the logarithm of both sides

• Square both sides

• Add 100 to both sides

• Multiply both sides by 1.39

Which logarithm is used in the example to solve the equation?

• Natural log

• Complex log

• Binary log

• Common log

What property of logarithms is applied to solve for T?

• Product property

• Change of base property

• Power property

• Quotient property

What is the exact solution of the equation in terms of logarithms?

• log(31) * log(1.39)

• log(31) + log(1.39)

• log(31) / log(1.39)

• log(1.39) / log(31)

What is the approximate value of T rounded to four decimal places?

• 10.4280

• 10.4000

• 10.4500

• 10.5000

What is the purpose of using a calculator in this process?

• To check for errors

• To get a decimal approximation

• To find the exact solution

• To graph the equation

Why is there a slight discrepancy when checking the solution?

• Due to using a different logarithm base

• Because of a calculation error

• Due to rounding the solution to four decimal places

• Because the equation is incorrect

What should the approximate value be when substituting back into the original equation?

• -3,200

• -3,083

• -3,100

• -3,000