`5^(6x) = 8320` Solve the equation accurate to three decimal places

Tuesday, January 5, 2010

$\displaystyle{{5}}^{{{6}{x}}}={8320}$ Solve the equation accurate to three decimal places

For exponential equation: $\displaystyle{{5}}^{{{6}{x}}}={8320}$ , we may apply the logarithm property:

$\displaystyle{\log{{\left({{x}}^{{y}}\right)}}}={y}\cdot{\log{{\left({x}\right)}}}.$

This helps to bring down the exponent value.

Taking "log" on both sides:

$\displaystyle{\log{{\left({{5}}^{{{6}{x}}}\right)}}}={\log{{\left({8320}\right)}}}$

$\displaystyle{6}{x}\cdot{\log{{\left({5}\right)}}}={\log{{\left({8320}\right)}}}$

Divide both sides by log (5) to isolate "6x":

$\displaystyle\frac{{{6}{x}\cdot{\log{{\left({5}\right)}}}}}{{{\log{{\left({5}\right)}}}}}=\frac{{{\log{{\left({8320}\right)}}}}}{{{\log{{\left({5}\right)}}}}}$

$\displaystyle{6}{x}=\frac{{{\log{{\left({8320}\right)}}}}}{{{\log{{\left({5}\right)}}}}}$

Multiply both sides by $\displaystyle\frac{{1}}{{6}}$ to isolate x:

$\displaystyle{\left(\frac{{1}}{{6}}\right)}\cdot{6}{x}=\frac{{{\log{{\left({8320}\right)}}}}}{{{\log{{\left({5}\right)}}}}}\cdot{\left(\frac{{1}}{{6}}\right)}$

$\displaystyle{x}=\frac{{{\log{{\left({8320}\right)}}}}}{{{6}{\log{{\left({5}\right)}}}}}$

x=0.935

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Tuesday, January 5, 2010

$\displaystyle{{5}}^{{{6}{x}}}={8320}$ Solve the equation accurate to three decimal places

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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?

Tuesday, January 5, 2010

Solve the equation accurate to three decimal places

No comments:

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?

$\displaystyle{{5}}^{{{6}{x}}}={8320}$ Solve the equation accurate to three decimal places

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