Then,
Thus,
Raise both sides to (-1) thus,
Here are some log questions that I haven't been able to solve. The problem that I'm having is that the base is different in some of them which is throwing me off.
By the way, the first question has a little typo. The right side of the equation should say 2log9(x-3) instead of 2log5(x-3)
If you can't see that picture then here's a link:
http://img133.imageshack.us/img133/2...0132021kf7.png
Hello Sportsfreund,
your calculator "knows" the logarithms to the base 10 (that's the log-button) and the logarithms to the bease e (that's th ln-button).
You can transform the different logarithms by using the log or the ln-function of your calculator:
.
According to your correction you'll solve:
I use the above mentioned formula:
Multiply by ln(3):
. This equation has no real solution.
I assume that there is maybe another typo.
EB
Alright, here's the answer to that typo question, by the way, you do change the exponent to 9:
logbase3(x+9)=logbase3(x-3)^2/log9base3
2logbase3(x+9)^2 - logbase3(x-3)^2=0
logbase3(x+9)^2/(x-3)^2=0
x^2-6x+9=x^2+18x+81
24x=-72
x=-3
I know that that's hard to follow but I think it's right.
hello Sportsfreund,
it isn't so hard to follow your calculations. You calculated correctly. Nevertheless x = -3 is not a solution of your equation:
I copy the line where I can show you why:
"logbase3(x+9)=logbase3(x-3)^2/log9base3"
Now plug in x = -3. You'll get
logbase3(-3+9)=logbase3(-3-3)^2/log9base3
which is the same as
logbase3(6)=logbase3(-6)^2/log9base3
And it is impossible to calculate the logarithm of a negative number. Thus x = -3 is not a solution of your equation.
So sorry to disappoint you.
EB