Chapter 10: Q. 196 (page 1034)

In the following exercises,solve each logarithmic equation.
$\log_{2} (5 x + 1) = 4$

Short Answer

Expert verified

The solution is $x = 3$ .

Step by step solution

Step 1.Given information

Consider the logarithmic equation $\log_{2} (5 x + 1) = 4$

The logarithmic from $y = \log_{a} x$ is equivalent to exponential form $x = a^{y}$ .

Step 2.Solve the given logarithmic equation.

Comparing $\log_{2} (5 x + 1) = 4$ with the standard form $y = \log_{a} x$ ,you have $y = 4, a = 2, x = 5 x + 1$

Convert logarithmic equation in exponential equation as shown below

$x = a^{y} 5 x + 1 = 2^{4} 5 x + 1 = 16$

So,the solution is $5 x + 1 = 16$

Now solve the equation as

$5 x + 1 - 1 = 16 - 1 [s u b s t r a c t 1] 5 x = 15 \frac{5 x}{5} = \frac{15}{5} [d i v i d e b y 5] x = 3$

So,the solution is $x = 3$

Step 3.Check

To check the solution,replace a by 3 in original equation

$\log_{2} (5.3 + 1) = 4 [x = 3] \log_{2} 16 = 4 2^{4} = 16 16 = 16 [t r u e]$

Therefore,the solution is $x = 3$

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In the following exercises,solve each logarithmic equation.
$\log_{2} (5 x + 1) = 4$

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve the given logarithmic equation.

Step 3.Check

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In the following exercises,solve each logarithmic equation.log25x+1=4

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve the given logarithmic equation.

Step 3.Check

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In the following exercises,solve each logarithmic equation.
$\log_{2} (5 x + 1) = 4$