Log5(x) = 16logx(5) solve for x

  • Thread starter TyErd
  • Start date
  • #1
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log5(x) = 16logx(5)
solve for x.

With this one, I have no idea where to start. All I have even thought about doing is bringing up the 16 to make it 5^16 but that doesn't seem to help me.
 

Answers and Replies

  • #2
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Convert one of your logs so that both logs are in the same base. Do you have a formula for converting from one log base to another?
 
  • #3
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No i dont have a formula to do that
 
  • #4
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the formula is:

log5(x) = log (x) / log (5)
 
  • #5
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Let y = logbx
Then x = by
So log x = log(by) = y log b
And y = (log x)/(log b)

Hence logbx = (log x)/(log b)

In the third step above, you can use any log base you want. I used the common log (log10).
 
  • #6
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ok thnx for the formulas, ok so i have the log base for one side which is (log10(x)) / (log10(5)) what do i do now?
 
  • #7
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Replace log5(x) in your original equation.

When you do that, what does your equation become?
 
  • #8
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(log10(x)) / (log10(5)) = logx(5^16)
 
  • #9
34,305
5,947


ok thnx for the formulas, ok so i have the log base for one side which is (log10(x)) / (log10(5)) what do i do now?
Instead of changing log5 to log, why don't you change logx to log5? The goal is to be using the same log base on both sides of the equation.
 
  • #10
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so are you saying change it so it is: log5(5^16) / log5(x) = log5(x) ????
 
  • #11
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Yes. Now put it in the context of the original equation.

log5x = logx516
==> log5x = [log5516]/log5x

The numerator on the right can be simplified to just plain 16, and you can multiply both sides by log5x.
 
  • #12
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omg, thankyou so much! i get it finally. I wish i could think like you
 
  • #13
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Practice...
 

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