Question
Solve for $t$ using natural logarithms.$$e^{3 t}=100$$
Solve for $t$ using natural logarithms. $$e^{3 t}=100$$
Answers
Solve the exponential equation algebraically. Approximate the result to three decimal places.
$4^{-3 t}=0.10$
So here's a question. We have 50 times e to the negative 0.12 t equals 10. It's all for tea in terms of ln and then put that into calculator and then we'll get her answer. So the first step is to isolate this tea As much as you can see, we're going to buy by 50 on both sides. I think it eats the natives. You're a 0.12 t equals one over five. So since we want to put this into turn in terms of natural logs frantic that Ellen on both sides and since these air in verses that cross out make it natives, your 0.12 t equals Ellen. But one of perfect, further isolating T we're go to bye bye. Negative 0.12 We got t you with Helen of one over five divided by I think it is your 0.12 So this is calculated ready for him, and this is approximates to about 13.4 12 And that's your answer
All right. Wrong question in 3 58 and the instructions tell us to solve, um, by using common log. So for even used common log. First thing I'm gonna do is divide both sides by e 1000. So that's gonna leave us with 1.3 to the Power T is equal to five. Okay. And then we can take uncommon log of both sides like it instructed us to do. So. Log, er 1.3 to the T is equal to log off. Five. From here, we can make our t value a cowfish. It so t log of 1.3 is equal to a log of five. And we'll divide both sides by log of 1.3 Great. And when you plug this into your calculator, they asked us to round three places. So we're gonna get approximately 54.449 as our final answer
Our own question 360 your directions holds to solve by using common log. First thing I'm gonna do, though, is we're gonna divide both sides by three to give us 1.4 to the power of three. T is equal to a machine. Ever leave it as 8/3 For now, I don't want around too early, because then my my decimal places might become a little bit off. Okay, So if we take the common long of both sides, it allows us to use our law properties to try to get this to be solved for T. So what I can do is I can take this explode right here, make it a coefficient in front of our common law. So we're gonna end up with three t times. Common log of 1.4 is equal to common law of a divided by three, and we can solve from here. So let's divide everything by three. We've got tea times common log of 1.4 Well, I was messy. It was, you know, four equal to law of 8/3 over three on. We also need to divide by log of 1.4 Great. So that's gonna leave us with tea is equal to, um I did write out this whole dust bowl. We only around thio the nearest ce thousands place. So you probably all need to write to, like, the 100 thousands place just to be safe. But I did write up the whole Dustin. Also log of 8/3 is 0.4 to 59 68732 I was just using a calculator where I could not see that value. So if you have a calculator that allows you to just say that value so you can divide it, then that's even better in the Dominator. Three times love of 1.4 I got 0.51100 018 again. Probably a lot of unnecessary place values. But when we divide that way around to, um, hunt the thousands place, then we get approximately 8.336 for our value of tea.
All right. Wrong question. 3 62 Problem. Asked us to solve using natural walk. Okay, first thing we're gonna do is divide both sides by 50. That's gonna give us E to the negative. 0.12 T is equal to 0.2. Okay. Hey, Maciste used natural log. So natural log of E to the negative 0.12 Tea is equal to natural log. Uh, 0.2. We know that natural log and either xar inverse operations of each other. So that's gonna leave us with negative 0.12 t is equal to the natural law of 0.2 and we can go ahead and divide both sides by negative as you're a point, too. To be left with tea, um, is equal to this is I wrote, um, several places behind the desk mole. Just because I cannot say that on the calculator I was using and I wanted to make sure that I got the right answer. So I did write lots of decimal places there. You don't want around too. Too early because then Ah, a couple of your decimal place starting to be off, so I did write several places, but if your calculator saves that number for you, that's perfect. Just save it. Divided by negative 0.2. So we get approximately 13.412 for our value of teeth.