Rearrange Logs: Get Guidance to Find F1 Value

[Physics Dad]

Please excuse my ignorance for posting this question, but I am confusing myself here. All I want to know is if I am rearranging this equation properly to find the value required...

Question
I want to rearrange the following equation to make F₁ the subject.

Equations
m₁-m₂=-2.5log₁₀(F₁/F₂)

My Thinking

So rearranging the above formula for F₁ it becomes:

F₁=10^{-(m₁-m₂)/2.5} x F₂

When it comes to rearranging logs (one of the most straight forward and simple things, I know) I find myself easily confused.

Please don't tell me the correct arrangement if I am wrong, just a little guidance please.

Thank you in advance!

 

[berkeman]

Equations
m1-m2=-2.5log10(F1/F2)

My Thinking

So rearranging the above formula for F1 it becomes:

F1=10-m2/2.5 x F2

That doesn't look right to me.

Start by moving the -2.5 to the LHS. Then you have log_10() on the RHS, so raise both sides to 10^() to get rid of the log term...

 

[Physics Dad]

Thanks,

So basically raise everything to ¹⁰, get rid of the logs, rearrange, take everything to the ¹⁰√ ?

F₁=-F₂(m₁-m₂/2.5)

Or is that silly?

 

[berkeman]

Thanks,

So basically raise everything to ¹⁰, get rid of the logs, rearrange, take everything to the ¹⁰√ ?

F₁=-F₂(m₁-m₂/2.5)

Or is that silly?

No, not close. Try showing each step that I mention in my first reply, and then continue with the algebra after that. Please show each step separately so we can check it.

 

[Physics Dad]

OK, thanks...

So here goes:

m₁-m₂=-2.5log₁₀(F₁/F₂)

-(m₁-m₂)/2.5=log₁₀(F₁/F₂)

F₁/F₂=10^{-(m₁-m₂)/2.5}

Is this right so far?

 

[berkeman]

OK, thanks...

So here goes:

m₁-m₂=-2.5log₁₀(F₁/F₂)

-(m₁-m₂)/2.5=log₁₀(F₁/F₂)

F₁/F₂=10^{-(m₁-m₂)/2.5}

Is this right so far?

Yes!

 

[Physics Dad]

so to finish it off it would be:

F1=(F₂)(10^{-(m₁-m₂)/2.5})

?

 

[haruspex]

so to finish it off it would be:

F1=(F₂)(10^{-(m₁-m₂)/2.5})

?

Yes.

 

[Physics Dad]

That's great, thank you so much for your help here.

I am sure it was frustrating for you, but it really helped me!