Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Solve each inequality for x.

$$(a)\ln x<0 \quad \text { (b) } e^{x}>5$$

(a) $0< x<1$(b) $x>\ln 5$

Calculus 1 / AB

Chapter 1

Functions and Sequences

Section 5

Logarithms; Semilog and Log-Log Plots

Functions

Missouri State University

Baylor University

University of Nottingham

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

08:04

Solve each inequality for …

01:02

01:46

00:41

Solve each inequality.…

00:55

Solve each equation or ine…

02:47

01:20

01:26

Solve the inequality.$…

01:45

Solving Inequalities Solve…

02:37

? Solving Inequalities Sol…

lawn of X is less than zero. That is the inequality you want to try to solve. So when it says this solving a call whenever you see that instruction, regardless of what the inequality is you're trying to isolate X, you're trying to get it by itself. And so in order to do that, we have to remove this lawn. So what we have to think about is what is the inverse operation of lawn? How do how do I remove the lawn? And the way you do that is by using this rule of law algorithms, which says that if you have log of some base B of a number, let's say a and it's equal to some number. See that you can rewrite that statement. So if you have a log on one side and a number on the other, you can rewrite as an exponential, and what you do is you take the base, so whatever that base happens to be, we're gonna call it base is be for now. But it's always gonna be some number, and in our case, the natural log rhythm is based E, and then you raise it to the exponents So you say B to the sea. You kind of think about it this way is equal to a So in order to remove the lager them in this question. What we're gonna do is we're just gonna rewrite it as e, which is our base raised to that exponents zero, and that's going to give us the number. And then we simply figure out what is eating zero on evens. Here was one. So our answer from removing the logger them is axe is less than one. But that's not quite the final answer because we have to consider lawn or any log rhythm is not allowed to be negative. And the reason is not a levee negative. You think graphically, longer them's looked like this. They have a vertical ash into their they don't ever cross zero. So you kind of think photographically you can see why negatives might be a problem. And if you think about it in this context, in this rule that we just talked about, you can also see why negatives to be a problem, I think, because if you take the base and it's positive and all the bases are that we use longer than is for. And no matter what you raise it to, then it's an exponents. You can never get a negative number from a positive base, Raceman exponents. You can't do that mathematically, and so we can't have negative. So we have to add in a stipulation, saying X has to also be greater than zero. And that's my solution. The lawn X is less than zero. It's remove the wog rhythm by writing as an exponential men solving. Now, the second part of this question, part beast, is e to the X is greater than five, and I want to know the solution to that. So it's a slightly different take on the same rule we know we just wrote down that log base B of A is equal to see means that hey is beat of the sea. So in the first part, in part A. We used this to this. We went from the logger them to the exponential. In this question, we're actually gonna go from the exponential to the logger them. So the base is E. This is my exponents X, and that's the number that I end up with. That's the value so what I'm gonna do. He is. I'm gonna rewrite this now as a log rhythm. So this is the exponents of X becomes greater than log of the base, which is e and then of that number five. So we just then can write. This log base is written as a natural longer than it has its own statement as lawn five. So my answer is X has to be greater than lawn five. So we're using the same rule in the first case just to quickly recap We took the log rhythm and wrote it as an exponential to solve this. And in the second case, we took the exponential and Rodas of lager than to solve it.

View More Answers From This Book

Find Another Textbook

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

$$(a)1< e^{3 x-1}<2 \quad \text {…

Solve each inequality for $x .$$$\text { (a) }1<e^{3 x-1}<2 \q…

(a) $ 1< e^{3x - 1} < 2 $(b) …

Solve each inequality.$$3+\ln x>e^{x}$$

Solve each equation or inequality.$e^{2 x}>5$

Solve each inequality.$$\left(e^{x}-2\right)\left(e^{x}-3\right)<2 e^…

Solve each inequality.$$5 \log x+2>0$$

Solve the inequality.$$x^{2} e^{x}-2 e^{x}<0$$

Solving Inequalities Solve the inequality.$$x^{2} e^{x}-2 e^{x}<0$$

? Solving Inequalities Solve the inequality.$$x^{2} e^{x}-2 e^{x}<…

02:26

The graph of a function $f$ is given. Estimate $\int_{0}^{8} f(x) d x$ using…

00:23

The graph of $g$ is shown. Estimate $\int_{-3}^{3} g(x) d x$ with six subint…

01:09

Find two positive numbers whose product is 100 and whose sum is a minimum.

04:28

Find the equilibria of the difference equation and classify them as stable o…

00:42

Evaluate the indefinite integral.$\int \frac{d x}{5-3 x}$

04:56

Logistic difference equation Illustrate the results of Example 4 for the log…

00:37

9-12 Use the Midpoint Rule with the given value of n toapproximate the i…

01:12

$n ^ { \prime } = \left( e ^ { - t } - 1 \right) n \quad n ( 0 ) = n _ { 0 }…

00:19

Use the Midpoint Rule with the given value of n toapproximate the integr…

02:00

When you turn on a hot-water faucet, the temperature $T$ of the water depend…

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.