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Chapter 5: Q. 77 (page 284)

solve each equation. Verify your results using a graphing utility.
$e^{x} = e^{3 x + 8}$

Short Answer

Expert verified

The value of x for which the above equation is valid is :

$- 4$

Step by step solution

01

Step 1. Given equation

$e^{x} = e^{3 x + 8}$

02

Step 2. Solving exponentially

$e^{x} = e^{3 x + 8} x = 3 x + 8 2 x = - 8 x = - 4$

03

Step 3. Verifying Graphically

Sketching the graphs of

$e^{x} & e^{3 x + 8}$

Where they will intersect will be the solution

Hence verified

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Most popular questions from this chapter

In Problems 61–72, the function f is one-to-one. Find its inverse and check your answer.

$f (x) = - \frac{2 x}{x - 1}$

If $f (x) = 2 x^{2} + 5$ and $g (x) = 3 x + a$ , find $a$ so that the graph of $f \circ g$ crosses the y-axis at 23.

Find the domain of the function $f (x) = \frac{x^{2} - 1}{x^{2} - 25}$ .

solve each equation. Verify your results using a graphing utility.

$4^{x} 2^{x^{2}} = 16^{2}$

A function $y = f (x)$ is increasing on the interval $(0, 5) .$ What conclusions can you draw about the graph of $y = f^{- 1} (x)$ ?

See all solutions

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