Question

Solve for x, if log2 (1 – 1/2*) = x - 2.
​

Answer 1

Question:-

Solve:-

$log_{2}(1 - \frac{1}{2} ) = x - 2$

Required Formulae:-

${a}^{ - m} = \frac{1}{ {a}^{m} }$

$log( {a}^{m} ) = m log(a)$

$log_{a}(a) = 1$

Solution:-

Given,

$log_{2}(1 - \frac{1}{2} ) = x - 2$

$log_{2}( \frac{1}{2} ) = x - 2$

$log_{2}( {2}^{ - 1} ) = x - 2$

$- 1 log_{2}(2) = x - 2$

$- 1 = x - 2$

$x = - 1 + 2 = > 2 - 1$

$x = 1$

So,the value of x is 1