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

Wednesday, May 22, 2013

$\displaystyle{\log}_{{2}}{\left(\frac{{1}}{{8}}\right)}$ Evaluate the expression without using a calculator.

$\displaystyle{\log}_{{2}}{\left(\frac{{1}}{{8}}\right)}$

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:

$\displaystyle={\log}_{{2}}{\left(\frac{{1}}{{{2}}^{{3}}}\right)}$

Then, apply the negative exponent rule $\displaystyle{{a}}^{{-{m}}}=\frac{{1}}{{{a}}^{{m}}}$ .

$\displaystyle={\log}_{{2}}{\left({{2}}^{{-{3}}}\right)}$

To simplify this further, apply the logarithmic rule $\displaystyle{\log}_{{b}}{\left({{a}}^{{m}}\right)}={m}\cdot{\log}_{{b}}{\left({a}\right)}$ .

$\displaystyle=-{3}\cdot{\log}_{{2}}{\left({2}\right)}$

Take note that when the base and argument of a logarithm are the same, the resulting value is 1 $\displaystyle{\left({\log}_{{b}}{\left({b}\right)}={1}\right)}$ .

$\displaystyle=-{3}\cdot{1}$

$\displaystyle=-{3}$

Therefore, $\displaystyle{\log}_{{2}}{\left(\frac{{1}}{{8}}\right)}=-{3}$ .

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Wednesday, May 22, 2013

$\displaystyle{\log}_{{2}}{\left(\frac{{1}}{{8}}\right)}$ Evaluate the expression without using a calculator.

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Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Wednesday, May 22, 2013

Evaluate the expression without using a calculator.

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Post a Comment

Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle{\log}_{{2}}{\left(\frac{{1}}{{8}}\right)}$ Evaluate the expression without using a calculator.

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?