Simultaneous Equations With Indices Problem

Any set of equations in the same variables are simultaneous equations. This is an example of simultaneous equations with indices.
\[100 \times 10^x=10^{2y}\]

\[\frac{10 \times 10^x}{10^y}=100\]

We can write the first of the as  
\[10^2 \times 10^x=10^{2y} \rightarrow 2+x=2y\]

We can write the second of these as  
\[\frac{10^1 \times 10^x}{10^y}=10^2 \rightarrow 1+x-y=2\]

We now have the equations
Thje first of these minus the second gives  
\[(2+x)-(1+x-y)=2y-2 \rightarrow 1+y=2y-2 \rightarrow 1+2=2y-y \rightarrow y=3\]
  into (1) then  

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