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Solve for $x.$$$e^{\ln (2 x-7)}=3$$

$$5$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Missouri State University

McMaster University

Baylor University

University of Michigan - Ann Arbor

Lectures

00:41

Solve the equation.$$e…

02:46

Solve the given equation f…

02:37

Solve for $x$ using logs.<…

01:36

Solve for $x$ using logs. …

00:19

Solve for $x$ without usin…

01:24

Solve the equation.$14…

00:44

Solve the following equati…

02:22

Solve each equation for $x…

00:32

Solve each equation.

eso There's one underlying concept in this problem that makes this fairly easy. Thio solve is equal to three. And that underlying concept is that e to the natural log. Uh, they're inverse functions, so they undo each other. Um, and so basically, what that boils down to is the left side is literally equal to two X minus seven on the right side stays alone, you know, stays. The same thing is equal to three eso. The whole underlying concept is that these air inverse functions and they undo each other, which, you know, braces down to this this fairly easy problem, because now all you have to do is add seven over to get two X is equal to 10. And then your last step is to divide both sides by two and then well, tended by by two is five. You could double check that. This is correct, because if you plug in five in here two times five is ah, 10 minus seven is three natural log of three. It's some number, but if you take e to that, some number will under the natural log, and you'll get back to three. So this is your answer

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