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Chapter 5: Q. 80 (page 284)

Solve given equation and verify your result using graphing utility.

(e4)x.ex2=e12

Short Answer

Expert verified

The solution set is{2,-6} and it is verified through graph.

Step by step solution

01

Step 1. Given information 

The given equation is :

(e4)x.ex2=e12

We have to solve for x and verify using graphing utility.

02

Step 2. Get a single expression with base e on both sides. 

Using law of exponents , get a single expression with base e on left side .

(e4)x.ex2=e4x.ex2=e4x+x2

03

Step 3. Comparing the expressions having same bases and solving for x . 

Since bases are same , therefore the exponential powers should also be the same.

4x+x2=12x2+4x-12=0

Factorise above expression

(x+6)(x-2)=0x+6=0,x-2=0x=-6,x=2

04

Step 4. Verification using graphing utility  

Graph

Y1=e4x+x2Y2=e12

Determine the point of intersection.

The graph intersects at x=2,x=-6

So the solution set is{2,-6}

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