Algebra II : Logarithms and exponents

Study concepts, example questions & explanations for Algebra II

varsity tutors app store varsity tutors android store

Example Questions

Example Question #2972 : Algebra Ii

, with  positive and not equal to 1.

Which of the following is true of  for all such  ?

Possible Answers:

Correct answer:

Explanation:

By definition,

If and only if

Square both sides, and apply the Power of a Power Property to the left expression:

It follows that for all positive  not equal to 1,

 

for all .

Example Question #2 : Logarithms

What is the value of  that satisfies the equation  ?

Possible Answers:

Correct answer:

Explanation:

 is equivalent to . In this case, you know the value of  (the argument of a logarithmic equation) and b (the answer to the logarithmic equation). You must find a solution for the base.

Learning Tools by Varsity Tutors