# Math Help - Student in need of a little help inverting a logarithmic problem

1. ## Student in need of a little help inverting a logarithmic problem

Hi!

My name is Cleo, I'm 19 years old and I am stuck on this little problem here. If anyone could help me, that would be absolutely wonderful.

I started with this:

111 = 17 + (13^(1/x)-1)*((550-17): (420^(1/x)-1))

and rewrote it to

533*13^(1/x) = 94*420^(1/x) + 439

But now I'm a little lost... How do I find my x?

2. ## Re: Student in need of a little help inverting a logarithmic problem

Originally Posted by cleomauritsz
Hi!

My name is Cleo, I'm 19 years old and I am stuck on this little problem here. If anyone could help me, that would be absolutely wonderful.

I started with this:

111 = 17 + (13^(1/x)-1)*((550-17): (420^(1/x)-1))

and rewrote it to

533*13^(1/x) = 94*420^(1/x) + 439

But now I'm a little lost... How do I find my x?

Goeien avond!

1. This sign ":" means division, right?

2. I doubt that you can find a solution in closed form . So use Newton's method to find an approximate result.

3. I've got $x \approx 2.512523062$

3. ## Re: Student in need of a little help inverting a logarithmic problem

Goedenavond!

The : stands for division, like you said. The point with this problem is, I have a whole list of different observations and for each set, I need to determine the x. The one above is just an example, that's why I'd like to find out how to do it step-by-step... The original problem is A = (B-C)/(420^(1/x)-1)*D^(1/x)+E-(B-C)/(420^(1/x)-1)

4. ## Re: Student in need of a little help inverting a logarithmic problem

Originally Posted by cleomauritsz
Goedenavond!

The : stands for division, like you said. The point with this problem is, I have a whole list of different observations and for each set, I need to determine the x. The one above is just an example, that's why I'd like to find out how to do it step-by-step... The original problem is A = (B-C)/(420^(1/x)-1)*D^(1/x)+E-(B-C)/(420^(1/x)-1)
In the attachment you find my result of the transformations of the given equation. Certainely you have found these proportions too.

I'm not able to solve the equation for x en het spijt mij!