`log_10(1000) = x` Solve for x or b

Friday, January 11, 2013

$\displaystyle{\log}_{{10}}{\left({1000}\right)}={x}$ Solve for x or b

$\displaystyle{\log}_{{10}}{\left({1000}\right)}={x}$

To solve, express the 1000 in terms of 10.

$\displaystyle{\log}_{{10}}{\left({10}\cdot{10}\cdot{10}\right)}={x}$

$\displaystyle{\log}_{{10}}{\left({{10}}^{{3}}\right)}={x}$

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

$\displaystyle{3}\cdot{\log}_{{10}}{\left({10}\right)}={x}$

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

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

$\displaystyle{3}={x}$

Therefore, the value of x is 3.

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Friday, January 11, 2013

$\displaystyle{\log}_{{10}}{\left({1000}\right)}={x}$ Solve for x or b

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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?

Friday, January 11, 2013

Solve for x or b

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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?

$\displaystyle{\log}_{{10}}{\left({1000}\right)}={x}$ Solve for x or b

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