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solve 3^2^x=195

 Jan 22, 2015

Best Answer 

 #2
avatar+33665 
+10

Or it could be 3^(2^x) = 195 in which case

 

Take logs:

(2^x)ln(3) = ln(195) or 2^x = ln(195)/ln(3)

 

Take logs again:

xln(2) = ln( ln(195)/ln(3) )

 

x = ln( ln(195)/ln(3) )/ln(2)

 

$${\mathtt{x}} = {\frac{{ln}{\left({\frac{{ln}{\left({\mathtt{195}}\right)}}{{ln}{\left({\mathtt{3}}\right)}}}\right)}}{{ln}{\left({\mathtt{2}}\right)}}} \Rightarrow {\mathtt{x}} = {\mathtt{2.262\: \!941\: \!541\: \!431\: \!602\: \!2}}$$

.

 Jan 22, 2015
 #1
avatar+130536 
+5

I assume this is (3^2)^x = 195  ??? if so, we have

9^x = 195     take the log of both sides

log 9^x  = log 195   and by a log property, we have

x log 9  = log 195    divide both sides by log 9

x = log 195 / log 9  = about 2.4

 

 Jan 22, 2015
 #2
avatar+33665 
+10
Best Answer

Or it could be 3^(2^x) = 195 in which case

 

Take logs:

(2^x)ln(3) = ln(195) or 2^x = ln(195)/ln(3)

 

Take logs again:

xln(2) = ln( ln(195)/ln(3) )

 

x = ln( ln(195)/ln(3) )/ln(2)

 

$${\mathtt{x}} = {\frac{{ln}{\left({\frac{{ln}{\left({\mathtt{195}}\right)}}{{ln}{\left({\mathtt{3}}\right)}}}\right)}}{{ln}{\left({\mathtt{2}}\right)}}} \Rightarrow {\mathtt{x}} = {\mathtt{2.262\: \!941\: \!541\: \!431\: \!602\: \!2}}$$

.

Alan Jan 22, 2015

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