Unknown indice using logarithms

**BG5965** · November 22nd 2008, 04:26 AM

Please help me with this logarithm equation:

Thanks - solve in terms of x.

**earboth** · November 22nd 2008, 04:34 AM

Originally Posted by BG5965

Please help me with this logarithm equation:

Thanks - solve in terms of x.

$\log_2\left(2^{2x}-56\right) - x=0~\implies~\log_2\left(2^{2x}-56\right) = x$

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

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

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

You'll get:

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

You only can use the second solution:

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

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