Solving Exponential Equations with Logarithms

The video tutorial explains how to solve an equation for T using base 10 logarithms. It begins by introducing the problem and rewriting the equation in both exponential and logarithmic forms. The tutorial then demonstrates how to transform the equation to isolate T, adding 3 to both sides and dividing by 2. Finally, the solution is verified, ensuring the correct application of logarithmic principles.

What is the initial form of the equation given in the video?

• T = (log10(7)+3)/2

• 2T-3 = log10(7)

• log10(7) = 2T-3

• 10^(2T-3) = 7

What does the equation 10^(2T-3) = 7 imply about the relationship between 10 and 7?

• 10 times (2T-3) equals 7

• 10 is raised to the power (2T-3) to equal 7

• 7 times (2T-3) equals 10

• 7 is raised to the power (2T-3) to equal 10

What does converting the equation into logarithmic form allow us to do?

• Multiply both sides by 2

• Simplify the equation

• Isolate the variable T

• Eliminate the variable T

What base is used for the logarithm in the equation?

• Base 3

• Base 7

• Base 2

• Base 10

What is the result of adding 3 to both sides of the logarithmic equation?

• 2T = log10(7) + 3

• log10(10) = 2T - 3

• log10(7) = 2T + 3

• log10(7) + 3 = 2T

What mathematical operation is performed after converting to logarithmic form?

• Subtraction

• Division

• Addition

• Multiplication

How do we solve for T after simplifying the equation?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 3 from both sides

• Add 2 to both sides

What is the purpose of dividing the entire equation by 2?

• To isolate T

• To eliminate T

• To multiply T

• To subtract from T

What is the final expression for T as solved in the video?

• (log10(7) + 3) * 2

• 3 / (log10(7) + 2)

• 2 / (log10(7) + 3)

• (log10(7) + 3) / 2

How is the correctness of the solution verified in the video?

• By using a calculator

• By checking the original equation

• By consulting a textbook

• By checking the answer box