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

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..

Answer Link

DelcieRiveria DelcieRiveria · Answer 2 · 2019-06-06T09:01:48+02:00

Answer:

The correct option is 2.

Step-by-step explanation:

The given logarithmic equation is

[tex]\log_2(x)+\log_2(x+7)=3[/tex]

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

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

[tex]x^2+7x-8=0[/tex]

[tex](x+8)(x-1)=0[/tex]

[tex]x=-8,1[/tex]

At x=1,

[tex]\log_2(1)+\log_2(1+7)=3[/tex]

[tex]0+3=3[/tex]

[tex]3=3[/tex]

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

At x=-8,

[tex]\log_2(-8)+\log_2(-8+7)=3[/tex]

[tex]\log_2(-8)+\log_2(-1)=3[/tex]

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.