# math question, solving for x when i know the exponent and the answer **URL:** \ **Category:** Factual Questions\ **Created:** [October 29, 2004, 3:55am UTC](https://boards.straightdope.com/t/math-question-solving-for-x-when-i-know-the-exponent-and-the-answer/271798 "2004-10-29T03:55:08Z")\ **Posts on this page:** 7\ **Page:** 2
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [October 29, 2004, 2:59pm UTC](https://boards.straightdope.com/t/math-question-solving-for-x-when-i-know-the-exponent-and-the-answer/271798/21 "2004-10-29T14:59:02Z")
> [@Jinx](#): > > So, in general, when solving problems such as the OP, do you use ln? or log? And, if it’s ln (natural log) how do we know this? If ln, then how did “e” enter into the problem…and, why doesn’t base 10 work? It seems counterintuitive that base 10 wouldn’t work…when our whole number system is based on powers of ten. - Jinx The procedure spelled out by **wolf\_meister** will work just fine whether you’re using logs to the base e (natural logs), to the base 10 (common logs), or any other base—as long as you’re consistent! ---
**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\ **Post date:** [October 29, 2004, 3:04pm UTC](https://boards.straightdope.com/t/math-question-solving-for-x-when-i-know-the-exponent-and-the-answer/271798/22 "2004-10-29T15:04:08Z")
> [@Jinx](#): > > So, in general, when solving problems such as the OP, do you use ln? or log? And, if it’s ln (natural log) how do we know this? If ln, then how did “e” enter into the problem…and, why doesn’t base 10 work? It seems counterintuitive that base 10 wouldn’t work…when our whole number system is based on powers of ten. - Jinx Either one works. log[sub]7[/sub], log[sub]143[/sub], log[sub]2.6[/sub], log[sub]1/3[/sub] would also work. You only need to be consistent. If you take, say, log[sub]2.6[/sub], then you have to use 2.6[sup]to the power of something[/sup] at the end, not 10[sup]to the power of something[/sup] or e[sup]to the power of something[/sup], etc. ---
**Author:** ![moriah](https://avatars.discourse-cdn.com/v4/letter/m/b2d939/32.png) [@moriah](https://boards.straightdope.com/u/moriah)\ **Post date:** [October 29, 2004, 6:23pm UTC](https://boards.straightdope.com/t/math-question-solving-for-x-when-i-know-the-exponent-and-the-answer/271798/23 "2004-10-29T18:23:04Z")
> [@Ivar](#): > > I have the following > .96=x[sup].05[/sup] > > what’s the manipulation to solve for x? > > IOW, .96sup[/sup]=x Let’s spell out the algebraic solution, step by step. First, we know that (x)[sup][a][sup]b[/sup][/sup] = (x)[sup][ab][/sup] And so, we want x[sup].05[/sup] wind up being x[sup]1[/sup] which is simply x. So, converting the decimal to fractions (algebra hates decimals), we have… x[sup]1/20[/sup] And to make that x[sup]1[/sup], will need to multiply 1/20 by 20. And to do that, we’ll have to raise both sides of the equation to the 20th power. .96[sup]20[/sup] = xsup[sup]20[/sup][/sup] ~.442 = x[sup](1/20 \* 20) [/sup] ~.442 = x[sup]1[/sup] = x ---
**Author:** ![moriah](https://avatars.discourse-cdn.com/v4/letter/m/b2d939/32.png) [@moriah](https://boards.straightdope.com/u/moriah)\ **Post date:** [October 29, 2004, 9:15pm UTC](https://boards.straightdope.com/t/math-question-solving-for-x-when-i-know-the-exponent-and-the-answer/271798/24 "2004-10-29T21:15:59Z")
Hmmmm… upon further reflection… I’ve used up all my math expertise and can’t answer this next question: Could the answer also be negative .442? ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [October 29, 2004, 9:27pm UTC](https://boards.straightdope.com/t/math-question-solving-for-x-when-i-know-the-exponent-and-the-answer/271798/25 "2004-10-29T21:27:57Z")
> [@moriah](#): > > Hmmmm… upon further reflection… I’ve used up all my math expertise and can’t answer this next question: > > Could the answer also be negative .442? Sure. ---
**Author:** ![Snarky\_Kong](https://avatars.discourse-cdn.com/v4/letter/s/a183cd/32.png) [@Snarky\_Kong](https://boards.straightdope.com/u/Snarky_Kong)\ **Post date:** [October 29, 2004, 11:38pm UTC](https://boards.straightdope.com/t/math-question-solving-for-x-when-i-know-the-exponent-and-the-answer/271798/26 "2004-10-29T23:38:53Z")
> [@Bryan Ekers](#): > > Sure. Care to explain this? I know if you’ve got something like 4=x^2 then x can be either 2 or -2, but isn’t this analagous to the case of 4=x^1/2? In that case x is going to be 4 and not -4. (-.442)^.05 should be a multiple of i which is not equal to .96. ---
**Author:** ![Thudlow\_Boink](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/thudlow_boink/32/320_2.png) [@Thudlow\_Boink](https://boards.straightdope.com/u/Thudlow_Boink)\ **Post date:** [October 30, 2004, 1:58am UTC](https://boards.straightdope.com/t/math-question-solving-for-x-when-i-know-the-exponent-and-the-answer/271798/27 "2004-10-30T01:58:47Z")
Right, **Snarky\_Kong**. If x were negative, x[sup]1/20[/sup] would not be a real number. [Previous page](https://boards.straightdope.com/t/math-question-solving-for-x-when-i-know-the-exponent-and-the-answer/271798.md?page=1)