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3^(x+1)*2=108

 Nov 16, 2019
 #1
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3^(x + 1)* 2  =  108     divide both sides by 2

 

3^(x + 1) =   54            take the log of both sides

 

log 3^(x+ 1)   = log 54      and we can write

 

(x + 1) log 3   = log 54         divide both sides by  log 3

 

x + 1  =   log54 / log 3       subtract 1 from both sides

 

x  = log 54 / log 3  - 1  ≈  2.63

 

However.....if this is supposed to be

 

3^[ (x + 1) * 2 ]   =  54

 

3^( 2x + 2)  =  54

 

3^(2x) * 3^2   = 54

 

3^(2x) * 9  = 54      divide both sides by  9

 

3^(2x)  =  6       take the log of both sides

 

log 3 ^(2x)  = log 6

 

(2x) log 3   = log 6

 

2x  = log6 / log 3

 

x =  log 6 / [2 log 3]

 

x = log 6 / [ log 3^2]

 

x = log 6 / log 9  ≈  .8155

 

 

 

cool cool cool

 Nov 16, 2019

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