Chapter 10: Q. 200 (page 1034)

In the following exercises, solve each logarithmic equation.
$\log_{4} (5 x + 6) = 3$

Short Answer

Expert verified

The solution is $x = 11.6$ .

Step by step solution

Step 1. Rewrite in exponential form and simplify.

Consider the logarithmic equation $\log_{4} (5 x + 6) = 3$ . Its equivalent exponential form is given as

$4^{3} = 5 x + 6$

On simplifying we get,

$64 = 5 x + 6$

Step 2. Solve for x

Subtract $6$ from both sides.

$\begin{array}{rcl} 64 - 6 & = & 5 x + 6 - 6 \\ 58 & = & 5 x \end{array}$

Divide both sides by $5$ .

$\begin{array}{rcl} \frac{58}{5} & = & \frac{5 x}{5} \\ 11.6 & = & x \end{array}$

Step 3. Check the solution

Substitute $11.6$ for $x$ in the original equation, we get

$\begin{array}{rcl} \log_{4} (5 x + 6) & = & 3 \\ \log_{4} (5 \times 11.6 + 6) & = & 3 \\ \log_{4} (58 + 6) & = & 3 \\ \log_{4} (64) & = & 3 \\ 4^{3} & = & 64 \\ 64 & = & 64 \end{array}$

So we get a true statement, thus the found solution is correct.

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In the following exercises, solve each logarithmic equation.
$\log_{4} (5 x + 6) = 3$

Short Answer

Step by step solution

Step 1. Rewrite in exponential form and simplify.

Step 2. Solve for x

Step 3. Check the solution

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In the following exercises, solve each logarithmic equation.log45x+6=3

Short Answer

Step by step solution

Step 1. Rewrite in exponential form and simplify.

Step 2. Solve for x

Step 3. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

In the following exercises, solve each logarithmic equation.
$\log_{4} (5 x + 6) = 3$