SOLUTION: find the value of x if: log5 + log(x+2) - log(x-1) = 2

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Question 1062603: find the value of x if: log5 + log(x+2) - log(x-1) = 2
Found 2 solutions by Edwin McCravy, Theo:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!


Use the log property:   
on the first two terms on the left side:



Distribute to get 



Use the log property:   
on the two terms on the left side:



Use the log property:  If  then 





Multiply both sides by x-1



Distribute on the right:



Subtract 100x from both sides:



Subtract 10 from both sides



Divide both sides by -95



Reduce fraction and a negative divided 
by a negative is positive:



Edwin
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
start with:

log(5) + log(x+2) - log(x-1) = 2

subtract log(5) from both sides to get:

log(x+2) - log(x-1) = 2 - log(5)

since log(2) = 100, this becomes:

log(x+2) - log(x-1) = log(100) - log(5)

this is equivalent to:

log((x+2)/(x-1)) = log(100/5) which is equal to:

log((x+2)/(x-1)) = log(20)

this is true if and only if (x+2)/(x-1) = 20

solve for x to get x = 22/19.

replace x with 22/19 in your original equation and you will see that the equation is true.

you will get log(5) + log(60/19) - log(3/19) = 2

evaluate this using your calculator to get 2 = 2.

this confirms your solution is correct.

your solution is x = 22/19.


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