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# Solve for x

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380
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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 Dec 7, 2017

### 2+0 Answers

#1
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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

Dec 7, 2017
#2
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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   Dec 7, 2017