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

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.

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.

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.