Changing bases Convert the following expressions to the indica...

Question

Changing bases Convert the following expressions to the indicated base.

$\ln ∣ x ∣$ using base 5

Accepted Answer

Welcome back, everyone. We write the expression Ln of the absolute value of X using base eight, we're given for answer choices which give us possible expressions. Now, first of all, before we solve this problem, we want to recall the conversion formula. Let's suppose that we begin with a logarithm with base A of number B, we can always convert that base A as follows. Let's suppose that we choose a new base, which is C. So we get log C a new base of number B divided by log of the same base C. This is our desired base of number A and this is the formula that we want to use. In this case, we're given Ln of X which we can rewrite as log of base E of the absolute value of X. From here, we first of all notice that our base A is equal to E and our B value from the formula is equal to the absolute value of X. So if we use these in our formula, we can say that log of base E of the absolute value of X is going to be equal to log. Now the C value is going to be eight because that's our desired base. So we get log eight of B, right? And our B is the absolute value of X. We're going to divide that by log of eight again. And now we're taking the value of A, which is E, right. Well, then we have the final expression. If we look at the answer choices, we notice that option A is the correct choice log base eight of the absolute value of X divided by a log base eight of E. So our final answer to this problem is option A. Thank you for watching.

Changing bases Convert the following expressions to the indicated base.

$\ln ∣ x ∣$ using base 5

Key Concepts

Change of Base Formula

Natural Logarithm

Absolute Value in Logarithms

Watch next