# Answer this Calc Log question for me plz

**URL:** <https://boards.straightdope.com/t/answer-this-calc-log-question-for-me-plz/378055>\
**Category:** Factual Questions\
**Created:** [October 27, 2006, 1:44am UTC](https://boards.straightdope.com/t/answer-this-calc-log-question-for-me-plz/378055 "2006-10-27T01:44:19Z")\
**Posts on this page:** 4\
**Page:** 1

<div class="post-metadata">

**Author:** ![Surbey](https://avatars.discourse-cdn.com/v4/letter/s/4491bb/32.png) [@Surbey](https://boards.straightdope.com/u/Surbey)\
**Post date:** [October 27, 2006, 1:44am UTC](https://boards.straightdope.com/t/answer-this-calc-log-question-for-me-plz/378055/1 "2006-10-27T01:44:19Z")

</div>

My sister has an ACT pretest that she is working on and it presents this problem

log(2) 24 – log(2) 3 = log(5) x  
() represents subscripts  
We know that x = 125 but how do ya prove it?

---

<div class="post-metadata">

**Author:** ![treis](https://avatars.discourse-cdn.com/v4/letter/t/bc79bd/32.png) [@treis](https://boards.straightdope.com/u/treis)\
**Post date:** [October 27, 2006, 2:39am UTC](https://boards.straightdope.com/t/answer-this-calc-log-question-for-me-plz/378055/2 "2006-10-27T02:39:12Z")

</div>

You have to use the change of base rule:

log(2)24=log(5)24/log(5)3

Then solve as normal.

---

<div class="post-metadata">

**Author:** ![A.I.Wintermute](https://avatars.discourse-cdn.com/v4/letter/a/7bcc69/32.png) [@A.I.Wintermute](https://boards.straightdope.com/u/A.I.Wintermute)\
**Post date:** [October 27, 2006, 4:03am UTC](https://boards.straightdope.com/t/answer-this-calc-log-question-for-me-plz/378055/3 "2006-10-27T04:03:49Z")

</div>

**treis** , I think your denominator there should be log(5)2, but even with that change I’m not sure I see how changing base simplifies the problem.

The solution I suspect is intended for an ACT problem is to make use of the fact that log x/y = log x - log y .

Reversing this rule, log(2) 24 – log(2) 3 becomes log(2) 24/3 or log(2) 8. Knowing that 8 = 2^3, we have log(2) 2^3, and the inverse functions log(2) x and 2^x cancel out, simplifying the left hand side of the equation to 3.

Now we have 3 = log(5) x, and raising 5 to the power of each side of the equation, 5^3 = x.

---

<div class="post-metadata">

**Author:** ![Surbey](https://avatars.discourse-cdn.com/v4/letter/s/4491bb/32.png) [@Surbey](https://boards.straightdope.com/u/Surbey)\
**Post date:** [October 28, 2006, 5:16am UTC](https://boards.straightdope.com/t/answer-this-calc-log-question-for-me-plz/378055/4 "2006-10-28T05:16:40Z")

</div>

[QUOTE=A. I. Wintermute]  
**treis** , I think your denominator there should be log(5)2, but even with that change I’m not sure I see how changing base simplifies the problem.

The solution I suspect is intended for an ACT problem is to make use of the fact that log x/y = log x - log y .

Reversing this rule, log(2) 24 – log(2) 3 becomes log(2) 24/3 or log(2) 8. Knowing that 8 = 2^3, we have log(2) 2^3, and the inverse functions log(2) x and 2^x cancel out, simplifying the left hand side of the equation to 3.

Now we have 3 = log(5) x, and raising 5 to the power of each side of the equation, 5^3 = x.  
[/QUOTE]

Thanks **A.I.Wintermute** although I already figured it out in my head on the way home from the movies today. Its amazing what listening to some good old Ska will make your brain do 😃 Thanks though, thats exactly how I did it in my head.