Please help me with this logarithm equation:

http://i301.photobucket.com/albums/nn74/BL5965/3d.png

Thanks - solve in terms of x.

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- Nov 22nd 2008, 04:26 AMBG5965Unknown indice using logarithms
Please help me with this logarithm equation:

http://i301.photobucket.com/albums/nn74/BL5965/3d.png

Thanks - solve in terms of x. - Nov 22nd 2008, 04:34 AMearboth
$\displaystyle \log_2\left(2^{2x}-56\right) - x=0~\implies~\log_2\left(2^{2x}-56\right) = x$

Now use the base 2 with both sides of the equation:

$\displaystyle 2^{2x}-56 = 2^x$

Use substitution $\displaystyle 2^x = y$ that means y > 0.

You'll get:

$\displaystyle y^2-y-56 = 0~\implies~y = -7~\vee~y=8$

You only can use the second solution:

$\displaystyle 8=2^x~\implies~x=3$