Exponential Functions and Properties

This video tutorial explores exponential and logarithmic functions, focusing on solving exponential equations using common bases. It covers advanced techniques for more complex problems, including negative exponents and fractions. The tutorial also delves into exponent properties and quadratic forms, providing a comprehensive understanding of these mathematical concepts.

What is the relationship between exponential and logarithmic functions?

• They are inverses of each other.

• They are both linear functions.

• They are the same.

• They are unrelated.

If 3^x = 3^7, what is the value of x?

• x = 21

• x = 7

• x = 3

• x = 1

How can 125 be expressed as a power of 5?

• 5^2

• 5^3

• 5^4

• 5^5

What is the prime factorization of 81?

• 2^4

• 3^3

• 2^3

• 3^4

What happens to a base when it has a negative exponent?

• It becomes a fraction.

• It becomes zero.

• It becomes negative.

• It remains the same.

How can 1/8 be expressed using a negative exponent?

• 8^1

• 8^-1

• 2^-3

• 2^3

What is the exponent property used when multiplying powers with the same base?

• Add the exponents.

• Multiply the exponents.

• Divide the exponents.

• Subtract the exponents.

In a quadratic form of an exponential equation, what is typically done first?

• Add all terms.

• Factor the equation.

• Multiply all terms.

• Divide all terms.