Exponential Equations Quiz

What is the solution to the equation 3^x = 81?

• x = 6

• x = 5

• x = 4

• x = 3

How do you express the square root of 2 as a rational exponent?

• 2^2

• 2^(-1/2)

• 2^(1/2)

• 2^1

What is the result of solving 4^x = 1/sqrt(2) using negative exponents?

• x = -2

• x = -1/2

• x = -1/4

• x = -1

When solving 27^(x+3) = 9^(x-1), what is the value of x?

• x = -9

• x = -11

• x = -5

• x = -7

Why is it important to double-check solutions in exponential equations?

• To ensure no calculation errors

• To verify the base is correct

• To confirm the exponent is positive

• To check for extraneous solutions

What is the inverse operation of the exponential function e^x?

• log base 10

• ln

• square root

• cube root

How can you solve 2^x = 5 using logarithms?

• Use cube root on both sides

• Use square root on both sides

• Use log base 2 on both sides

• Use ln on both sides

What is the result of solving 3^x = 5/8 using logarithms?

• x = ln(5/8) / ln(3)

• x = ln(3) / ln(5/8)

• x = ln(8) / ln(5)

• x = ln(5) / ln(8)

In the equation 3^(x-2) = 5^(3x+2), what is the first step to solve it using logarithms?

• Apply ln to both sides

• Apply log base 3 to both sides

• Apply square root to both sides

• Apply log base 5 to both sides

What is the purpose of using the greatest common factor in solving complex exponential equations?

• To simplify the equation

• To combine like terms

• To isolate the variable

• To factor out the variable