When are you supposed to take the natural log of both sides of an equation?

  • Thread starter Jurrasic
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  • #1
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It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?
 
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  • #2
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You use "e" to cancel out a natural log of an equation.
 
  • #3
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It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?
If you have an equation that involves exponents, that's a natural for taking the log of both sides.

For example, if ex + 2 = 3, we can take the natural log of both sides to get
ln(ex + 2) = ln(3)
x + 2 = ln(3)
x = -2 + ln(3) ≈ -1.307
 
  • #4
symbolipoint
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It seems this is done randomly, yet it must not be random, there must be some logic to it, but when do you know to do it? What is like a clue or the rules that indicate you can/should take the natural log of both sides of an equation?
The key to understand is you use an inverse operation or a sequence of inverse operations to reveal a formula for an unknown but sought variable. An exponential function is the inverse of a logarithmic function. You would do something similar if you wanted to clear for an additive inverse or a multiplicative inverse.

Mark44's example to illustrate is a good one.

Note that logb(bx)=x
 

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