I can't remember how to solve equations with logarithms/exponents

  • Context: High School 
  • Thread starter Thread starter Jamin2112
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Discussion Overview

The discussion revolves around solving equations involving logarithms and exponents, specifically focusing on the equation t2/t1 = (d2/d1)1.06 and the challenge of isolating d2. Participants explore different methods and approaches to tackle the problem, reflecting on their experiences with logarithmic identities and algebraic manipulation.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses frustration over forgetting how to solve logarithm problems after a year out of college and seeks help with isolating d2 in the given equation.
  • Another participant suggests taking the logarithm of both sides as a potential first step.
  • A question arises about whether to use log base 1.06 or another base.
  • Participants clarify that either log10 or natural logarithm (ln) can be used.
  • One participant proposes raising both sides of the equation to the 1/1.06 power as an alternative method.
  • Another participant reflects on their confusion and questions whether the initial suggestion was leading them astray.
  • Basic identities of logarithms are mentioned as potentially useful for solving the equation.
  • A different approach is suggested, emphasizing rearranging the equation to isolate d2 without starting with logarithms, using exponent rules instead.
  • One participant acknowledges that while starting with logs might seem harder, it is not significantly longer than the alternative method proposed.
  • Another participant provides a detailed breakdown of using natural logarithms to isolate d2, indicating that both approaches have merit.

Areas of Agreement / Disagreement

Participants exhibit a range of approaches to the problem, with some favoring logarithmic methods while others prefer algebraic manipulation. There is no consensus on a single method, and the discussion remains open to various interpretations and techniques.

Contextual Notes

Participants reference different logarithmic identities and rules, indicating potential limitations in their understanding or application of these concepts. There are also mentions of confusion regarding the initial suggestions and the clarity of the steps involved in isolating d2.

Jamin2112
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This is frustrating me so much. I've been out of college for 1 year and I already forgot how to solve logarithm problems (though, to my surprise, I've encountered one I need to solve in real life.)

t2/t1 = (d2/d1)1.06

and I need to solve for d2.

I know the equation is the equivalent of

logd2/d1(t2/t1) = 1.06,

but I still can't figure out how to isolate the d2.
 
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Jamin2112 said:
This is frustrating me so much. I've been out of college for 1 year and I already forgot how to solve logarithm problems (though, to my surprise, I've encountered one I need to solve in real life.)

t2/t1 = (d2/d1)1.06

and I need to solve for d2.

I know the equation is the equivalent of

logd2/d1(t2/t1) = 1.06,

but I still can't figure out how to isolate the d2.
Start by taking the log of both sides.
 
Mark44 said:
Start by taking the log of both sides.

log1.06 of both sides?
 
Raise both sides to the 1/1.06 power.

Chet
 
Chestermiller said:
Raise both sides to the 1/1.06 power.

Wow, I feel like an idiot now. Was Mark44 trying to lead me down a rabbit hole?
 
Jamin2112 said:
Wow, I feel like an idiot now. Was Mark44 trying to lead me down a rabbit hole?
No. Mark is a serious guy. He had a different approach in mind, probably motivated by your questions about logarithms.

Chet
 
Chestermiller said:
No. Mark is a serious guy. He had a different approach in mind, probably motivated by your questions about logarithms.

When I originally tried doing the "log to both sides, ..." approach, I started going in circles.
 
  • #10
Starting with logs seems like the hard way to me. Do what you usually do when you want to change the subject of a formula: get d2 on its own on one side.

First use the exponent rule: (a/b)^n = a^n/b^n, then re-arrange to get

d_2^1.06 = ...

Then continue.

EDIT: 'log rule' changed to 'exponent rule'
 
Last edited:
  • #11
qspeechc said:
Starting with logs seems like the hard way to me. Do what you usually do when you want to change the subject of a formula: get d2 on its own on one side.

First use the log rule: (a/b)^n = a^n/b^n, then re-arrange to get
That would be an exponent rule.
qspeechc said:
d_2^1.06 = ...

Then continue.
I agree that this approach is simpler, but taking logs of both sides isn't that much longer. After you take the natural log of both sides of the original equation, you have
$$ln(\frac{t_2}{t_1}) = 1.06 ln(\frac{d_2}{d_1})$$
Now divide both sides by 1.06 and exponentiate to get d2/d1 by itself. One more step and you're done.

The approach I suggested was just the first one to come to mind.
 
  • #12
Slip of the tongue, so to speak ...:p
 

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