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Chapter 5: Q 104. (page 299)

Solve the equation.
$\log_{5} (x^{2} + x + 4) = 2$

Short Answer

Expert verified

The solution to the equation, $\log_{5} (x^{2} + x + 4) = 2$ is, $x = \frac{- 1 + \sqrt{85}}{2}$ .

Step by step solution

01

Step 1. Given Information

The given equation to be solved is $\log_{5} (x^{2} + x + 4) = 2$ .

02

Step 2. Formula used

Rule of change from logarithm to exponents:

$\log_{a} b = y \Rightarrow a^{y} = b$

03

Step 3. Finding Solution

The given equation is $\log_{5} (x^{2} + x + 4) = 2$ .

Use rule of change from logarithm to exponents:

$\log_{5} (x^{2} + x + 4) = 2 x^{2} + x + 4 = 5^{2} x^{2} + x + 4 = 25 x^{2} + x - 21 = 0 x = \frac{- 1 \pm \sqrt{1 + 84}}{2} x = \frac{- 1 \pm \sqrt{85}}{2}$

The solution to the given equationis, $x = \frac{- 1 + \sqrt{85}}{2}$ .

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Most popular questions from this chapter

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

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

Ideal Body Weight One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function

$W (h) = 50 + 2.3 (h - 60)$

(a) What is the ideal weight of a $6$ -foot male?

(b) Express the height has a function of weight W.

(c) Verify that $h = W (h)$ is the inverse of $W = W (h)$ by showing that role="math" localid="1646158219737" $h (W (h)) = h$ and $W (h (W)) = W$ .

(d) What is the height of a male who is at his ideal weight of $80$ kilograms?

[Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given byrole="math" localid="1646159253780" $W (h) = 45.5 + 2.3 (h - 60)$ .

Begin with the graph of $y = e^{x}$ and use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

$f (x) = e^{x} - 1$

In Problems $33 - 40$ , the graph of an exponential function is given. Match each graph to one of the following functions.

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

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

See all solutions

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