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Chapter 10: Q. 303 (page 1054)

In the following exercises, solve for x

log5(x+1)+log5(x-5)=log57

Short Answer

Expert verified

By solving the equation log5(x+1)+log5(x-5)=log57, the value of xis 6

Step by step solution

01

Step 1. Given

An expressionlog5(x+1)+log5(x-5)=log57

To solve the expression forx

02

Step 2. Use the Product property

By Product Property of logarithm

logaM+logaN=logaMN

log5((x+1)(x-5))=log57log5(x2-4x-5)=log57

03

Step 3. Use One to One property

If logaM=logaN, then M=N

x2-4x-5=7x2-4x-12=0

04

Step 4. Solve the equation

x2-4x-12=0(x-6)(x+2)=0x=-2,6

Logarithm for a negative number does not exist.

So,x=6

05

Step 5. Check the solution

Substitute x=6in the original equation and solve.

log5(6+1)+log5(6-5)=log57log5(7)+log5(1)=log57log57=log57

Hence the solution is checked.

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