Wednesday, May 22, 2013

`log_2 (1/8)` Evaluate the expression without using a calculator.

`log_2 (1/8)`


To evaluate this, consider the base and argument of the logarithm. The base of the logarithm is 2. And the 8 can be expressed in terms of factor 2. So factoring 8, the expression becomes:


`= log_2 (1/2^3)`


Then, apply the negative exponent rule `a^(-m)=1/a^m` .


`= log_2 (2^(-3))`


To simplify this further, apply the logarithmic rule `log_b (a^m) = m * log_b (a)` .


`= -3 * log_2(2)`


Take note that when the base and argument of a logarithm are the same, the resulting value is 1 `(log_b (b) = 1)` .


`= - 3 * 1`


`= -3`



Therefore, `log_2 (1/8) = -3` .

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