+0  
 
0
198
2
avatar+589 

Solve for x

37x=81x+9

 

 

What is the exact value of x?

5*84x=375

 

 

What is the exponential form of the logarithmic equation?

log0.8 0.4096=4

 

jbouyer  Dec 7, 2017
 #1
avatar+7096 
+2

Solve for  x  .

 

37x  =  81x+9

 

Since   81  =  9 * 9   and   9  =  3 * 3  ,      81  =  3 * 3  * 3 * 3  =  34

 

37x  =  (34)x+9        Using the rule  (xa)b  =  xab  ......

 

37x  =  34x + 36       Now the bases are equal, so set the exponents equal.

                             We can also say this is taking the  log3  of both sides of the equation

7x  =  4x + 36

                             Subtract  4x  from both sides.

3x  =  36

                             Divide both sides by  3 .

x  =  12

hectictar  Dec 7, 2017
 #2
avatar+86944 
+3

5 * 8^(4x)  =  375      divide both sides by 5

 

8^(4x)  = 75     take the log of both sides

 

log 8 ^(4x)  [ log (75)    and we can write

 

(4x) log (8)  = log(75)       divide both sides by  4 log (8)

 

x =    log (75)  /  [ 4 log (8) ]

 

 

 

 

 0.8 4  =  0.4096

 

 

cool cool cool

CPhill  Dec 7, 2017

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