Question

Which of the following shows the true solution to the logarithmic equation solved below? HURRY!

Answer 1

The correct option is 2.

Explanation:

The given logarithmic equation is

`\log_2(x)+\log_2(x+7)=3`

`\log_2[x(x+7)]=3`
`[\because \log a+\log b=\log ab]`

`x(x+7)=2^3`
`[\because \log_ax=b\Rightarrow x=a^b]`

`x^2+7x-8=0`

`(x+8)(x-1)=0`

`x=-8,1`

At x=1,

`\log_2(1)+\log_2(1+7)=3`

`0+3=3`

`3=3`

LHS=RHS, therefore x=1 is a solution of given equation.

At x=-8,

`\log_2(-8)+\log_2(-8+7)=3`

`\log_2(-8)+\log_2(-1)=3`

Logarithmic functions are defined only for positive values. Therefore x=-8 is not a solution of given equation. It is also known as extraneous solutions.

Hence option 2 is correct.

Answer 2

Short Answer x = 1
There is nothing with the way the equation was solved. All the rules of logs were obeyed.

The problem is in the answer. Try putting log - 8 into your calculator. Do it like this if you are uncertain.

log
8
+/-
=
My calculator gives Error 2.

Rule values less than and including 0 do not have a logarithm..