Homework Help

Solve for x (1/3)^x = 724 Round your answer four decimals.

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted August 17, 2013 at 1:10 AM via web

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Solve for x

(1/3)^x = 724

Round your answer four decimals.

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llltkl | College Teacher | Valedictorian

Posted August 17, 2013 at 1:43 AM (Answer #1)

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To solve an equation containing a variable exponent, isolate the exponential quantity. Then take  natural (to the base e) log on both sides.

`(1/3)^x = 724`

`rArr 3^-x=724`

`rArr -xln3=ln724`

`rArr x=-ln724/ln3`

`rArr x=-5.993746~~-5.9937`

Therefore, the value of x is approximately -5.9937.

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Wiggin42 | TA , Grade 11 | Valedictorian

Posted June 29, 2014 at 8:46 PM (Answer #2)

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(1/3)^x = 724

Here we have the x in the exponent. So we'll have to do the opposite operation of exponents which is log. Take the log of both sides: 

log (1/3)^x = log724

A cool property of logs is that the exponent can now be written as multiplication like this: 

x log(1/3) = log724

Remember that log of anything is just a number. So: 

x = log724 / log(1/3)

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