Chapter 10: Q. 299 (page 1054)

In the following exercises, solve for $x$ .
$\log x + \log (x - 15) = 2$

Short Answer

Expert verified

By solving the equation $\log x + \log (x - 15) = 2$ , the value of $x$ is $20$

Step by step solution

Step 1. Given

An expression $\log x + \log (x - 15) = 2$

To solve the expression for $x$

Step 2. Use the Product property

By Product Property of logarithm,

$\log_{a} M + \log_{a} N = \log_{a} M N$

$\log (x (x - 15)) = 2$

Step 3. Rewrite in exponential form

$x (x - 15) = 10^{2}$

$x^{2} - 15 x = 100$

$x^{2} - 15 x - 100 = 0$

Solve the equation.

$x^{2} - 20 x + 5 x - 100 = 0 (x - 20) (x + 5) = 0 x = - 5, 20$

Logarithm for a negative number does not exist.

So, $x = 20$

Step 4. Check the solution

Substitute $x = 20$ in the original equation and solve.

$\log (20) + \log (20 - 15) = 2 \log (100) = 2$

$2 = 2$

Hence the equation has been checked.

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In the following exercises, solve for $x$ .
$\log x + \log (x - 15) = 2$

Short Answer

Step by step solution

Step 1. Given

Step 2. Use the Product property

Step 3. Rewrite in exponential form

Step 4. Check the solution

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In the following exercises, solve for x.logx+log(x-15)=2

Short Answer

Step by step solution

Step 1. Given

Step 2. Use the Product property

Step 3. Rewrite in exponential form

Step 4. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Mechanics Maths

Logic and Functions

Pure Maths

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, solve for $x$ .
$\log x + \log (x - 15) = 2$