Chapter 10: Q. 292 (page 1054)

In the following exercise, solve for x.
$\log_{5} (4 x - 2) = \log_{5} 10$

Short Answer

Expert verified

The solution of the given expression is $x = 3$

Step by step solution

Step 1. Given information.

The given expression $\log_{5} (4 x - 2) = \log_{5} 10$

Step 2. Use logarithmic properties

Using one to one property, we get:

$\log_{5} (4 x - 2) = \log_{5} 10 4 x - 2 = 10 4 x = 12$

Step 3. Solve for x.

Solving the equation, we get:

$4 x = 12 \frac{4 x}{4} = \frac{12}{4} [d i v i d i n g b o t h s i d e s b y 4] x = 3$

Step 4. Check the value

Substituting $x = 3$ in the given expression, we get:

$\log_{5} (4 x - 2) = \log_{5} 10 \log_{5} (4 \cdot 3 - 2) = \log_{5} 10 \log_{5} 10 = \log_{5} 10$

This is true.

Thus, $x = 3$ is the solution of the given function.

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In the following exercise, solve for x.
$\log_{5} (4 x - 2) = \log_{5} 10$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use logarithmic properties

Step 3. Solve for x.

Step 4. Check the value

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In the following exercise, solve for x.log5(4x−2)=log510

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use logarithmic properties

Step 3. Solve for x.

Step 4. Check the value

One App. One Place for Learning.

Most popular questions from this chapter

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Decision Maths

Theoretical and Mathematical Physics

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In the following exercise, solve for x.
$\log_{5} (4 x - 2) = \log_{5} 10$