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 Suppose 5^{3x+2} = 675. Find 5^x

cormier123  Jun 7, 2018
 #1
avatar+12566 
+1

Take LOG of both sides to get:

(3x+2) LOG 5 = LOG 675    solve for x

3x+2 = log 675/log5

x=.682606194

5^.682606194 =~3

ElectricPavlov  Jun 7, 2018
 #2
avatar+87629 
+1

Thanks, EP....here's a slighly different approach...

 

5^(3x + 2)  = 675     and we can write

 

5^2 * 5^(3x)  = 675      simplify

 

25 * 5^(3x)  = 675      divide both sides  by 25

 

5^(3x)  = 27     and we can write

 

(5^x)^3  = 27     take the cube root of both sides

 

5^x  = 3

 

 

cool cool cool

CPhill  Jun 7, 2018

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