Chapter 10: Q. 408 (page 1064)

In the following exercises, solve each logarithmic equation.
$\log_{2} (5 x - 7) = 3$

Short Answer

Expert verified

The solution is $x = 3$ .

Step by step solution

Step 1. Convert into exponential form

Consider the logarithmic equation $\log_{2} (5 x - 7) = 3$ .

Its equivalent exponential form is given as $2^{3} = 5 x - 7$ .

And it is simplified to

$8 = 5 x - 7$

Step 2. Solve the equation for x

To solve the equation add $7$ both sides.

$\begin{array}{rcl} 8 + 7 & = & 5 x - 7 + 7 \\ 15 & = & 5 x \end{array}$

Now divide both sides by $5$ .

$\begin{array}{rcl} \frac{15}{5} & = & \frac{5 x}{5} \\ 3 & = & x \end{array}$

Step 3. Check the solution

Substitute $3$ for $x$ in the original equation.

$\begin{array}{rcl} \log_{2} (5 x - 7) & = & 3 \\ \log_{2} (5 \times 3 - 7) & = & 3 \\ \log_{2} (15 - 7) & = & 3 \\ \log_{2} (8) & = & 3 \\ 2^{3} & = & 8 \\ 8 & = & 8 \end{array}$

As the statement is true, so the found solution is correct.

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In the following exercises, solve each logarithmic equation.
$\log_{2} (5 x - 7) = 3$

Short Answer

Step by step solution

Step 1. Convert into exponential form

Step 2. Solve the equation for x

Step 3. Check the solution

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In the following exercises, solve each logarithmic equation. log25x-7=3

Short Answer

Step by step solution

Step 1. Convert into exponential form

Step 2. Solve the equation for x

Step 3. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each logarithmic equation.
$\log_{2} (5 x - 7) = 3$