Logarithmic and Exponential Functions

The video tutorial covers solving various math problems, including conic sections, logarithmic equations, and exponent rules. It begins with completing the square to identify a conic section as a circle, followed by solving logarithmic equations using properties of logs. The tutorial also includes identifying errors in logarithmic simplification and verifying solutions to exponent problems.

What is the center of the circle represented by the equation x^2 + y^2 + 4x - 6y - 3 = 0 after completing the square?

• (-2, 3)

• (2, -3)

• (3, -2)

• (-3, 2)

What is the radius of the circle represented by the equation x^2 + y^2 + 4x - 6y - 3 = 0 after completing the square?

• 5

• 3

• 2

• 4

How can the equation 5^x = 17 be rewritten using logarithms?

• log_5(x) = 17

• log_10(17) = x

• log_5(17) = x

• log_10(x) = 17

What is the value of x if log_10(x) = -2?

• 100

• 0.1

• 0.01

• 10

Which equation is equivalent to log_3(1/9) = x?

• 3^x = 1/9

• 3^x = 9

• 3^x = 1/3

• 3^x = 3

What is the first incorrect step in simplifying log_4(4/64)?

• log_4(4) - log_4(8)

• log_4(4) - log_4(4)

• log_4(4) - log_4(64)

• log_4(4) - log_4(16)

In the problem involving x^3 * x^-7, which student correctly simplified the expression?

• Michael

• Shanan

• Brenda

• Jeremy

What is the correct simplification of x^3 * x^-7?

• 1/x^10

• x^4

• 1/x^4

• x^10

Which student made a mistake by treating x^-7 as x^7 in the denominator?

• Michael

• Jeremy

• Brenda

• Shanan

What is the correct exponent form of x^3 * x^-7?

• x^-4

• x^4

• x^10

• x^-10