# Thread: Unknown indice using logarithms

1. ## Unknown indice using logarithms

Thanks - solve in terms of x.

2. Originally Posted by BG5965

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:

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