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Chapter 5: Q 89. (page 299)

Solve the equation.
$\log_{2} (2 x + 1) = 3$

Short Answer

Expert verified

The solution to the equation, $\log_{2} (2 x + 1) = 3$ is, $x = 3.5$ .

Step by step solution

01

Step 1. Given Information

The given equation to be solved is $\log_{2} (2 x + 1) = 3$ .

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 $\log_{2} (2 x + 1) = 3$ .

Use rule of change from logarithm to exponents:

$\log_{2} (2 x + 1) = 3 2 x + 1 = 2^{3} 2 x = 8 - 1 x = \frac{7}{2} x = 3.5$

The solution to the given equationis, $x = 3.5$ .

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Most popular questions from this chapter

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.

$f (x) = 2 - e^{- x / 2}$

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

$A (n)$ ________ is a function of the form $f (x) = C a^{x}$ where $a > 0, a \neq 1,$ and $C \neq 0$ are real numbers. The base $a$ is a ____ and $C$ is a _____.

Solve the equation $3^{- x} = 81$

and verify your results using a graphing utility.

solve equation. Verify your results using a graphing utility.

$8^{- x + 14} = 16^{x}$

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

$f (x) = - \frac{3 x + 1}{x}$

See all solutions

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