Chapter 10: Q. 10.78 (page 1049)

Solve: $\log_{2} x + \log_{2} (x - 6) = 4$

Short Answer

Expert verified

By solving the equation, $\log_{2} x + \log_{2} (x - 6) = 4$ , the value of $x$ is $8$

Step by step solution

Step 1. Given

An expression $\log_{2} x + \log_{2} (x - 6) = 4$

To solve the expression

Step 2. Use the product property on LHS

Use the Product Property of logarithm

$\log_{a} M + \log_{a} N = \log_{a} (M N) \log_{2} x + \log_{2} (x - 6) = 4 \log_{2} (x (x - 6)) = 4$

Step 3. Rewrite in exponential form.

$\log_{2} (x (x - 6)) = 4 x^{2} - 6 x = 2^{4} x^{2} - 6 x - 16 = 0$

Step 4. Factorize the equation

$x^{2} - 6 x - 16 = 0 (x - 8) (x + 2) = 0 x = - 2, 8$

Logarithm for a negative number does not exist.

So, $x = 8$

Step 5. Check the solution

Substitute $x = 8$ in the original equation and solve.

$\log_{2} 8 + \log_{2} (8 - 6) = 4 \log_{2} (8) + \log_{2} (2) = 4 \log_{2} 16 = 4 4 = 4$

Hence the solution has been checked.

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Solve: $\log_{2} x + \log_{2} (x - 6) = 4$

Short Answer

Step by step solution

Step 1. Given

Step 2. Use the product property on LHS

Step 3. Rewrite in exponential form.

Step 4. Factorize the equation

Step 5. Check the solution

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Solve: log2x+log2(x-6)=4

Short Answer

Step by step solution

Step 1. Given

Step 2. Use the product property on LHS

Step 3. Rewrite in exponential form.

Step 4. Factorize the equation

Step 5. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Pure Maths

Calculus

Decision Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve: $\log_{2} x + \log_{2} (x - 6) = 4$