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# Logarithm Problems

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3^x - 3^-x = 6.832 >> Calculator has solved this question for me...however I cannot understand method used....Can you help

Guest Jun 23, 2017
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I'm not sure what method your calculator may use, but here's an approach

3^x  -  3^(-x)  = 6.832

3^x  -   1 / 3^x   =  6.832      multiply through by 3^x

3^(2x)   -  1  =  6.832 *  3^x       rearrange as

(3^x)^2 - 6.832 * 3^x  - 1  = 0

Let  3^x  = y       and we have that

y^2  - 6.832y  -  1  = 0

Solving this by using the quadratic formula we have that

y ≈  -0.143362     or    y ≈ 6.97536

Back-subsitutitng we have that

3^x  ≈   -0.143362     or     3^x  ≈ 6.97536

Since an exponenttial is never negative, reject the first solution....so....

3^x  ≈  6.97536   take the log of both sides

log 3^x  ≈  log 6.97536        and we can write

x *  log 3 ≈  log 6.97536        divide both sides by log 3

x  ≈   log 6.97536 / log 3  ≈   1.76803

CPhill  Jun 23, 2017
edited by CPhill  Jun 23, 2017

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