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Solve the equations. If necessary, round to the nearest ten-thousands. 

 

1) 4log32 - 2log3x = 1

 

2) logx= 2

Guest Mar 5, 2018
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1) 4log32 - 2log3x = 1

 

Note that  1   =  log3 3  .....so we can write

 

4 log3 2 - 2log3x  = log3 3      {  log property :  b log a  =  logab  }

 

log3 2^4  - log3x^2  = log33   { log a - log b  =  log (a/b) }   ⇒ 24  = 16

 

log3 (16/ x^2)  = log3 3

 

Since  we have equal logs   we can just solve

 

16/x^2  =  3

 

x^2  = 16 / 3         take the positive root 

 

x  =  4 / √ 3   ≈ 2.3094

 

 

2) logx2 = 2       ....we can write

 

2 log x  =  2         divide both sides by 2

 

log x  =  1

 

This says that    10^1  =  x  =  10

 

 

cool cool cool

CPhill  Mar 5, 2018
edited by CPhill  Mar 5, 2018

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