Solving Exponential and Logarithmic Equations

The video tutorial covers solving exponential and logarithmic equations, focusing on using common bases, logarithms, and rounding techniques. It includes examples of complex equations with operations, quadratic equations, and applying logarithmic rules like product and quotient rules. The tutorial emphasizes understanding the domain of logarithmic functions and checking solutions for accuracy.

What is the value of n if 6^n = 1/216?

• n = 1

• n = 3

• n = -3

• n = -1

If 81 is expressed as 3^4 and 343 as 3^5, what is the value of r in the equation 81^(-3r) = 343?

• r = 12/5

• r = -12/5

• r = -5/12

• r = 5/12

In the equation 5^(-8n) = 5^(-3n), what is the value of n?

• n = 5

• n = 0

• n = -1

• n = 1

What is the value of k if 2^(-16k) = 2^(-15k + 10)?

• k = 0

• k = 10

• k = -10

• k = 5

How do you solve the equation 10^(a+1) = 11 using logarithms?

• Use natural log and solve for a

• Take log base 10 of both sides and solve for a

• Directly equate a to 11

• Convert to base e and solve

What is the approximate value of a in the equation 10^(a+1) = 11?

• a = 0.041

• a = 1.041

• a = -0.041

• a = 0.104

In the equation log base 5 of (k^2 + 1) = log base 5 of (9k + 1), what are the possible values of k?

• k = 0 and k = 1

• k = 1 and k = 9

• k = 9 and k = 10

• k = 0 and k = 9

How do you solve the equation log base 5 of (10 - 2x) = 1?

• Directly equate x to 5

• Use the product rule

• Use the quotient rule

• Convert to exponential form and solve for x

What is the solution for x in the equation log base 5 of (-x/9) = 1?

• x = 9

• x = -9

• x = 45

• x = -45

In the equation 2^(x^2 + 2) = 18, what are the possible values of x?

• x = ±4

• x = ±3

• x = ±5

• x = ±2