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Chapter 10: Q. 299 (page 1054)

In the following exercises, solve for x.

logx+log(x-15)=2

Short Answer

Expert verified

By solving the equation logx+log(x-15)=2, the value of xis 20

Step by step solution

01

Step 1. Given

An expression logx+log(x-15)=2

To solve the expression for x

02

Step 2. Use the Product property

By Product Property of logarithm,

logaM+logaN=logaMN

log(x(x-15))=2

03

Step 3. Rewrite in exponential form

x(x-15)=102

x2-15x=100

x2-15x-100=0

Solve the equation.

x2-20x+5x-100=0(x-20)(x+5)=0x=-5,20

Logarithm for a negative number does not exist.

So, x=20

04

Step 4. Check the solution

Substitute x=20in the original equation and solve.

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

2=2

Hence the equation has been checked.

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