SOLUTION: Solve for x: log5 x + log5(x-24) = 2 Please show me how you got the answer, thanks.

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Question 1130364: Solve for x:
log5 x + log5(x-24) = 2
Please show me how you got the answer, thanks.

Found 3 solutions by josgarithmetic, MathLover1, greenestamps:
Answer by josgarithmetic(39630)   (Show Source): You can put this solution on YOUR website!







, but NOT the other solution

Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

............use the rule

........change the base


...if log same, we have


........factor





solutions:
if ->
if ->-> disregard negative solution; , then for any negative number
so, your solution is:



Answer by greenestamps(13215)   (Show Source): You can put this solution on YOUR website!




You have two valid and correct solutions to your equation from other tutors; let me suggest a different method that I personally find easier.

My preferred first step, given two terms with log base 5 on the left and an integer on the right, is to rewrite the integer as a term in log base 5:



Now, with all terms log base 5, I can convert this to an ordinary algebraic equation using basic rules of logarithms; then solve the equation:




or

However, the log of a negative number is not a real number, so the only solution is x = 25.

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