Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Solve each inequality for x.
(a) $ \ln x < 0 $(b) $ e^x > 5 $
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Official textbook answer
Video by Heather Zimmers
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 1 / AB
Calculus 2 / BC
Functions and Models
Inverse Functions and Logarithms
Functions of Several Variables
Johns Hopkins University
Harvey Mudd College
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.
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.
Solve each inequality for …
Solve the inequality for $…
$55-56$ Solve each inequal…
$51-52$ Solve each inequal…
Solve each inequality.…
Solve each equation or ine…
$39-40$ Solve each inequal…
Solve the inequality analy…
Solve the inequality.$…
I'm going to solve both of these inequalities algebraic Lee and then confirmed them graphically. So first of all, with natural log of X is less than zero. I'm going to use a process called exponentially ating, which means that each side of the equation or each side of the inequality will be an exponents on the same base. And I'm going to use based E. So we hav e raised to the left side of the inequality is less than e raised to the right side of the inequality. And we should know, based on inverse functions that e to the natural log of X simplifies to just be X, and each of zero is one, so we have X is less than one. There's one other thing we need to consider, though. Remember the domain of along with Mick Function X has to be greater than zero. So we do have X is less than one, and we have X is greater than zero. When you combine those together, you get zero is less than X is less than one now. Graphically, if you think about what the natural log of X function looks like, it looks like this with the next intercept at one. Where is it greater than zero Down here. We're sorry. Less than zero down here that that's where the Y values are. Less than zero. And that was between X equals zero and X equals one. Okay, now let's do something similar to the other inequality. And I'm going to take the natural log of both sides. So we have natural log of e to the X is greater than natural law. Go five because of inverse functions. Natural log of each of the X simplifies to just be x so x is greater than natural log five.
View More Answers From This Book
Find Another Textbook
Toe median annual income In a certain town is $54,000, A sample median of 56…
A recent poll found that 30% of those surveyed are worried about aggressive …
The lengths of human pregnancies are normally distributed with a mean of 4 =…
TakTank DFigure 1: 2 Tank SystemYou have two tanks, Tank A, whic…
Age of first heart attack The horizontal axis is age. The vertical axis Is f…
Question 19Mint Wnetmtu !Fla qucxion100 pcoplc arc tested fo…
Imagine you survey your friends to find the kind movie they like best; the r…
new drug [s being proposed forthe treatmentof migraine hcadachex Unfortunatc…
Question # 4 Given a normally distributed population with a mean of 100 and …
A sociologist randomly selects single adults for different groups of three, …