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Chapter 5: Q. 58 (page 315)

Solve each exponential equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.

2路49x+11路7x+5=0

Short Answer

Expert verified

The given equation has no real solution.

Step by step solution

01

Step 1. Given information.

The given equation is:

2路49x+11路7x+5=0

It can be rewritten as:

2路(72)x+11路7x+5=02(7x)2+11(7x)+5=0

02

Step 2. Substitute another variable and solve for it.

Let 7x=u.

2u2+11u+5=02u2+10u+u+5=02u(u+5)+1(u+5)=0(2u+1)(u+5)=0

Use the zero product property.

2u+1=0oru+5=0u=-12oru=-57x=-12or7x=-5

The equations 7x=-12and 7x=-5have no solution because 7x>0.

03

Step 3. Verify the result by the graphing utility.

Plot the graph of y=2路49x+11路7x+5 on a coordinate plane. The x-intercept of the curve is the solution of the given equation.

The graph does not intersect thex-axis at any point. So, the given equation has no real solution.

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