SOLUTION: Solve the equation log3(x)-log3(x-5)=1 I tried like this: log3(x/x-5)=1 3=(x/x-5) 3*(x-5)=x 3x-15=x 2x=15 x=15/2 but the answer should be x=5/4, where did I go wrong?

Question 752631: Solve the equation log3(x)-log3(x-5)=1
I tried like this:
log3(x/x-5)=1
3=(x/x-5)
3*(x-5)=x
3x-15=x
2x=15
x=15/2
but the answer should be x=5/4, where did I go wrong?
Found 2 solutions by Theo, dkppathak:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you did nothing wrong.
the correct answer is x = 15/2.

you can use your calculator to confirm.

log3(x) = log10(x) / log10(3)

since log10 is the calculator LOG function, this can be reduced to:

log3(x) = LOG(x) / LOG(3)

your answer is x = 15/2 = 7.5

replace x in the original equation with 7.5 and you will get:

log3(7.5) - log3(7.5-2) = 1
this simplifies to:
log3(7.5) - log3(2.5) = 1

use the conversion factor to make this equation:

log(7.5)/LOG(3) = LOG(2.5)/LOG(3) = 1

use your calculator to get:

1.8340437671 - .8340437671 = 1

this simplifies to 1 = 1.

Answer by dkppathak(439) (Show Source): You can put this solution on YOUR website!
yes you are correct for your solution
log (base3)x-log (base3)x-5=1
by using log formula
we can do as log (base3)x/x-5 =1
we can do it as
3 to the power 1= x/x-5
3=x/x-5
3x-15=x
3x-x =15
2x=15
x=15/2
x=7.5

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