Logarithmic and Exponential Concepts

The video tutorial explains how to solve an exponential equation, specifically 10 raised to the power of negative two x equals 12.4. It covers two main methods: using the common logarithm and converting the equation into a logarithmic form. The tutorial demonstrates solving for x both exactly and approximately, and verifies the solution using properties of logarithms.

What is the base of the given exponential equation?

• 12.4

• 10

• 5

• 2

Which method can be used to solve the exponential equation?

• Taking the common log of both sides

• Using quadratic formula

• Using trigonometric identities

• Taking the natural log of both sides

What is the equivalent logarithmic form of the equation 10^(-2x) = 12.4?

• log(12.4) = 2x

• log(10) = 12.4

• log(12.4) = -2x

• log(10) = -2x

How do you solve for x in the equation log(12.4) = -2x?

• Multiply both sides by 2

• Add 2 to both sides

• Divide both sides by -2

• Subtract 2 from both sides

What is the exact solution for x in terms of logarithms?

• x = -1/2 * log(12.4)

• x = -2 * log(12.4)

• x = 2 * log(12.4)

• x = log(12.4)

What is the approximate decimal value of x rounded to three decimal places?

• 0.457

• 0.547

• -0.457

• -0.547

Which property of logarithms is used to verify the solution?

• Base-exponent matching property

• Quotient property

• Product property

• Power property

What happens when the base of the exponent matches the base of the logarithm?

• The expression remains unchanged

• The expression simplifies to the number part of the logarithm

• The expression simplifies to one

• The expression simplifies to zero

What is the result of 10 raised to the power of log base 10 of 12.4?

• 0

• 10

• 12.4

• 1

Why is it important to verify the solution of an equation?

• To simplify the equation further

• To ensure the solution is correct

• To practice calculation skills

• To find alternative solutions