Thread: logarithmic equation

Solve for all real values of x:


$\displaystyle log_2{\bigg(x^{log_2x}\bigg)} \ = \ 4$




(The first "2" that you see on the farther left is supposed to be in a subscript position and act as base 2 for the logarithm.)

$\log_2(x^{\log_2(x)})=4$

$x^{\log_2(x)} = 16$

$2^{(\log_2(x))^2} = 16$

$\left(\log_2(x)\right)^2 = 4$

$\log_2(x) = \pm 2$

$x = 2^{\pm 2} = \dfrac 1 4,~4$

Originally Posted by greg1313

Solve for all real values of x:
$\displaystyle log_2{\bigg(x^{log_2x}\bigg)} \ = \ 4$

Another way:$\displaystyle log_2{\bigg(x^{log_2x}\bigg)} = \left(\log_2(x)\right)^2$