Logarithm state the value of x for which the equation is defined

In summary, the equation ##\ \log_x(5)+2\log_x2-\log_1/x2=3## is defined for certain values of x. The equation can be solved for x by using the change of base formula.
  • #36
Jaco Viljoen said:
$$\frac{\ln125}{\ln x}+\frac{\ln4}{\ln x}+\frac{\ln2}{\ln x}=3$$
$$\frac{\ln1000}{\ln x}=3$$I am not sure if I have done the right thing... Please advise
Yeah, this is correct.
Do, some further solving.
 
  • Like
Likes Jaco Viljoen
Physics news on Phys.org
  • #37
$$\frac{\ln125}{\ln x}+\frac{\ln4}{\ln x}+\frac{\ln2}{\ln x}=3$$
$$\frac{\ln1000}{\ln x}=3$$
$$ln1000=3lnx$$
ln(x)3=ln1000
x3=1000
103=1000
so x=10

Boom, done.

I don't think this change of base rule was covered in my manual.
Can this always be used?

Thank you
 
  • #38
SammyS said:
The base, b, must be positive, but can't be 1. ( I suppose Mark had a typo.)
That's what I meant, but was somehow unable to make my fingers follow the instructions from my brain. Thanks for pointing it out, Sammy! Embarassing, but I would rather see a mistake be corrected.

In my defense, the original equation had x as the base:
3logx5+2logx2-log1/x2=3
 
Last edited:
  • Like
Likes Jaco Viljoen
  • #39
Jaco Viljoen said:
I don't think this change of base rule was covered in my manual.
Can this always be used?

Thank you
You could use that anytime.Of whether it is useful or not depends on the situation and your thinking.
 
  • Like
Likes Jaco Viljoen
Back
Top