Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
Solve each inequality for x.
(a) $ 1< e^{3x - 1} < 2 $(b) $ 1 - 2 \ln x < 3 $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Mary Wakumoto
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
02:24
Jeffrey Payo
01:46
Heather Zimmers
Calculus 1 / AB
Calculus 2 / BC
Calculus 3
Chapter 1
Functions and Models
Section 5
Inverse Functions and Logarithms
Functions
Integration Techniques
Partial Derivatives
Functions of Several Variables
Johns Hopkins University
Campbell University
Oregon State University
University of Michigan - Ann Arbor
Lectures
04:31
A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
12:15
In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.
08:04
Solve each inequality for …
01:02
02:47
Solve each inequality.…
02:36
Find the values of $x$ tha…
02:54
Solve each equation or ine…
01:44
04:24
00:18
00:41
03:37
Solve each equation and in…
01:10
01:04
Solve each inequality alge…
00:29
Alright, it's time to solve some inequalities with exponential and log functions. This looks like fun. Alright, so let's take a look at a um we want to get the X out of the exponents so we can do that by doing the inverse function to E which is Ln Ln of every term. So we'll get L out of one Less than Ln of E to the three X -1 less. An Ln of two. Ln of one by the way is zero. Um Alright, so we get zero lesson member Ln of E. These are composite inverse functions. They undo each other mathematically and out pops the arguments. So we'll get three x minus one lesson Ln of two. Let's add one to every part. So that will give us L N two plus one. That will divide everything by three. So we get one third less than X less than Ln of two plus 1/3. So um as lovely. Let's fix that. Three. Make it look a little bit nicer. So that is then uh we were able to solve our inequality so we know what X has to be in between. So that worked well. Alright, awesome. Now we're gonna do part B, part B s, logs. So let's go ahead and start working. This first thing we'll do is subtract one from both sides. So we'll get -2. less than two when you divide by a negative. That changes the inequality. So we're going to divide by -2. That will give us Ln of X Greater than -1. Now we can do uh the inverse function that will get our argument out. So we're going to do to the L. N. Effects Greater than Edith and -1. So therefore access greater than E to the minus one and either minus one. We can write as one over E. So X is greater than one over E. So we have accomplished our task. Alright, have a great day. See you next time.
View More Answers From This Book
Find Another Textbook