Solve each equation. Give solutions in exact form. See Examples 5...

Question

Solve each equation. Give solutions in exact form. See Examples 5–9. 5 ln x = 10

Accepted Answer

Hey, everyone here we are asked to solve the logarithmic equation for X and provide an exact solution here. The given equation is 46 times the natural log of X is equal to 184. Here we have four answer choice options. Answer a, the solution set of E to the power of four, answer B, the solution set of negative E to the power of four and E to the power of four answer choice C, the solution set of negative E squared and E squared and answer choice D, the solution set of E squared. So here, as we recall, the given logarithmic equation is 46 times the natural log of X is equal to 184. So to begin solving for X, we first just want to get the natural log of X alone by dividing both sides by 46. And so now rewriting our equation, we have the natural log of X is equal to 184 divided by 40 six. Simplifying, we get that the natural log of X is equal to four. So now to get this equation as an equation of X, we need to recall that the natural log of X is equivalent to log base E of X. So now rewriting the left side of our equation so far, we now have log base E of X is equal to four. So now to get X alone, we need to recall that log base A of X is equal to Y has an equivalent form where X is equal to A to the power of Y. So we see that our equation so far is in the form where we have log base A of X is equal to Y. So we need to rewrite it in the second form where X is equal to A to the power of Y. Well, here we can see that going to just be X E, the value of A is going to be E and the value of Y is going to be four. So now rewriting we have X is equal to E to the power of four. So here we are, we were able to obtain a direct solution where X is equal to E to the power of four. So we can rewrite this as a solution set where again, we have a solution set of E to the power of four. So with this finalized solution set, we are left with answer choice. A where again, we have the solution set of E to the power of four. Thanks for watching. I hope you found this video. Helpful and I'll see you again next time.

Solve each equation. Give solutions in exact form. See Examples 5–9. 5 ln x = 10

Key Concepts

Natural Logarithm

Exponential Equations

Isolating the Variable

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