Can you show me how to solve this logarithmic equation? log(x-9)=1-logx?

Question

thanks Helmet, that gave me the number i was looking for.

Answer 1

Hopefully log means log to the base10.
If so, 1 = log(10)
log(x-9) = log(10) - log(x)
log(x-9) = log(10/x)
x - 9 = 10/x
x^2 - 9x - 10 = 0
(x - 10)(x + 1) = 0
x = - 1, 10
Reject - 1 since you cannot take the log of a negative number.

Answer 2

logx+log(x+one million)=log56 logx(x+one million) = log56 x(x+one million) = fifty six x^2+x = fifty six x^2+x-fifty six =0 (x+8)(x-7) = 0 x=-8 or x=7 subsequently x=7 is the only answer and ignore with regards to the answer x=-8 is as a results of the fact the logarithm of a destructive extensive type isn't plausible.

Answer 3

Since you have log on both sides of the equation and they both have the same base you can get rid of them. And then you are left with: x-9=x. So basically you just solve that for x.