Question
Points UDue Friday by &am Set 3.5: Change of Base Formula Problem Score: 3/4 4/4 answeredX Questionlast try: 0 of Pts. See Details for more_ Score on Next question You can retry this question belowlog_8(9) as 3 quotient of natural logarithms. RewriteSubmit Question
Points U Due Friday by &am Set 3.5: Change of Base Formula Problem Score: 3/4 4/4 answered X Question last try: 0 of Pts. See Details for more_ Score on Next question You can retry this question below log_8(9) as 3 quotient of natural logarithms. Rewrite Submit Question
Answers
Use the base-change formula to find each logarithm to four decimal places.
$$\log _{1 / 3}(3.5)$$
Okay, so we're asked to write this in terms of natural law. So use our change of basis formula. That is, if we have logged base A B. And that's equal to the natural log of B over the natural log obey. Okay, so for log based, three of dirty, that's the natural log of dirty over the natural log Abate. Okay, I'm not like this into I can't believe it. And I get that this is equal to three point Phil 95 nights.
Problem. We're going to express a given log rhythmic expression in terms of the natural longer them, and then use a calculator to find the exact value we start by running are longer given logarithmic expression. Log face three of 30. We know using log rules that we can write this as the natural log of 30 divided by the natural log of three. Using a calculator, this expression comes out to be equivalent to 3.9 59 and that is the answer tour logarithmic expression and also expressed in terms of natural logs.
We have log based three of 21 we're going to use the change of based formula to convert it to something that we can put into a calculator so we can change it to log based 10 or log based E. That would be common log or natural log. It doesn't matter which. So it would look like log of 21 over log of three if you change it to log based 10 Common log or it would look like natural log of 21 over natural log of three if you change it to natural log. And either way, you're going to put that in the calculator and we're gonna approximate that as 2.771
Using the change of base for belonged face three of 21. We would rewrite that as loved of 21 designed by law of three. Then we can do this our calculator. And you just have to make sure that when you're dividing it, you put the end parenthesis e there. So Ah, this becomes 2.77 one. Now most of you have a t I 84. You can do this problem right here. As it is, you go to mass scroll down a and it has logged with a different base. So then you would use that and you can get the same answer without using the change of face. If you have an older calculator, it does not have that feature. And you have to use a change of base form. Roll down a LA please.
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