`x^2 - x = log_5(25)` Solve for x or b

Thursday, February 25, 2010

$\displaystyle{{x}}^{{2}}-{x}={\log}_{{5}}{\left({25}\right)}$ Solve for x or b

$\displaystyle{{x}}^{{2}}-{x}={\log}_{{5}}{\left({25}\right)}$

First, simplify the right side of the equation. To do so, factor 25.

$\displaystyle{{x}}^{{2}}-{x}={\log}_{{5}}{\left({{5}}^{{2}}\right)}$

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

$\displaystyle{{x}}^{{2}}-{x}={2}\cdot{\log}_{{5}}{\left({5}\right)}$

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

$\displaystyle{{x}}^{{2}}-{x}={2}\cdot{1}$

$\displaystyle{{x}}^{{2}}-{x}={2}$

To solve quadratic equation, one side should be zero.

$\displaystyle{{x}}^{{2}}-{x}-{2}={0}$

Then, factor the left side.

$\displaystyle{\left({x}-{2}\right)}{\left({x}+{1}\right)}={0}$

Set each factor equal to zero. And isolate the x.

$\displaystyle{x}-{2}={0}$

$\displaystyle{x}={2}$

$\displaystyle{x}+{1}={0}$

$\displaystyle{x}=-{1}$

Therefore, the solution is $\displaystyle{x}={\left\lbrace-{1},{2}\right\rbrace}$ .

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Thursday, February 25, 2010

$\displaystyle{{x}}^{{2}}-{x}={\log}_{{5}}{\left({25}\right)}$ 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?

Thursday, February 25, 2010

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?

$\displaystyle{{x}}^{{2}}-{x}={\log}_{{5}}{\left({25}\right)}$ 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?