Solve for \(h\) in \(921\times {3}^{2}{({3}^{-127})}^{-2}-{27}^{h}=127\).
Solve for \(h\).
\[921\times {3}^{2}{({3}^{-127})}^{-2}-{27}^{h}=127\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[921\times {3}^{2}{(\frac{1}{{3}^{127}})}^{-2}-{27}^{h}=127\]
Simplify \({3}^{127}\) to \(3.930062\times {10}^{60}\).
\[921\times {3}^{2}{(\frac{1}{3.930062\times {10}^{60}})}^{-2}-{27}^{h}=127\]
Simplify \({3}^{2}\) to \(9\).
\[921\times 9{(\frac{1}{3.930062\times {10}^{60}})}^{-2}-{27}^{h}=127\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[921\times 9\times \frac{1}{{(\frac{1}{3.930062\times {10}^{60}})}^{2}}-{27}^{h}=127\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[921\times 9\times \frac{1}{\frac{1}{{(3.930062\times {10}^{60})}^{2}}}-{27}^{h}=127\]
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[921\times 9\times \frac{1}{\frac{1}{{3.930062}^{2}{({10}^{60})}^{2}}}-{27}^{h}=127\]
Simplify \({3.930062}^{2}\) to \(15.445384\).
\[921\times 9\times \frac{1}{\frac{1}{15.445384{({10}^{60})}^{2}}}-{27}^{h}=127\]
Use Power Rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[921\times 9\times \frac{1}{\frac{1}{15.445384\times {10}^{120}}}-{27}^{h}=127\]
Invert and multiply.
\[921\times 9\times 1\times 15.445384\times {10}^{120}-{27}^{h}=127\]
Simplify \(921\times 9\) to \(8289\).
\[8289\times 1\times 15.445384\times {10}^{120}-{27}^{h}=127\]
Simplify \(8289\times 1\) to \(8289\).
\[8289\times 15.445384\times {10}^{120}-{27}^{h}=127\]
Simplify \(8289\times 15.445384\) to \(128026.784639\).
\[128026.784639\times {10}^{120}-{27}^{h}=127\]
Subtract \(128026.784639\times {10}^{120}\) from both sides.
\[-{27}^{h}=127-128026.784639\times {10}^{120}\]
Multiply both sides by \(-1\).
\[{27}^{h}=-127+128026.784639\times {10}^{120}\]
Regroup terms.
\[{27}^{h}=128026.784639\times {10}^{120}-127\]
Use Definition of Common Logarithm: \({b}^{a}=x\) if and only if \(log_b(x)=a\).
\[h=\log_{27}{(128026.784639\times {10}^{120}-127)}\]
Use Change of Base Rule: \(\log_{b}{x}=\frac{\log_{a}{x}}{\log_{a}{b}}\).
\[h=\frac{\log{(128026.784639\times {10}^{120}-127)}}{\log{27}}\]
Use Power Rule: \(\log_{b}{{x}^{c}}=c\log_{b}{x}\)\(\log{27}\) -> \(\log{{3}^{3}}\) -> \(3\log{3}\).
\[h=\frac{\log{(128026.784639\times {10}^{120}-127)}}{3\log{3}}\]
Substitute \(h=\frac{\log{(128026.784639\times {10}^{120}-127)}}{3\log{3}}\) into \(\pi =\frac{2}{3}\).
Since \(\pi =\frac{2}{3}\) is not true, this is an inconsistent system.
