Let x=_282. Then, we must have 2^x = 82. Since 8=2^3 and 2 = 2^1/2, we have 2^x = 2^3 2^1/2 = 2^7/2. Therefore, x=72.

jmc

algebra intermediate

Problem

Evaluate

lo g_{2} 82

Solution

Let

x = lo g_{2} 82

. Then, we must have

2^{x} = 82

. Since

8 = 2^{3}

and

2 = 2^{1/2}

, we have

2^{x} = 2^{3} \cdot 2^{1/2} = 2^{7/2}

. Therefore,

x = \frac{7}{2}

Final answer

\frac{7}{2}