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avatar+88 

3^x+1=6^4-x

If your answer has logarithms use parenthesis for the numerator and the denominator,

for example:    x= (ln3-2ln4)/(-2ln3+ln4)

 Apr 11, 2015

Best Answer 

 #1
avatar+21508 
+15

If the problem is:  3x + 1  =  64 - x

--->   ln( 3x + 1 )  =  ln( 64 - x )

--->   (x + 1)ln(3)  =  (4 - x)ln(6)

--->   x·ln(3) + ln(3)  =  4·ln(6) - x·ln(6)

--->    x·ln(3) + x·ln(6)  =  4·ln(6) - ln(3)

--->   x[ ln(3) + ln(6) ]  =  4·ln(6) - ln(3)

--->  x  =  [ 4·ln(6) - ln(3) ] / [ ln(3) + ln(6) ]

 Apr 12, 2015
 #1
avatar+21508 
+15
Best Answer

If the problem is:  3x + 1  =  64 - x

--->   ln( 3x + 1 )  =  ln( 64 - x )

--->   (x + 1)ln(3)  =  (4 - x)ln(6)

--->   x·ln(3) + ln(3)  =  4·ln(6) - x·ln(6)

--->    x·ln(3) + x·ln(6)  =  4·ln(6) - ln(3)

--->   x[ ln(3) + ln(6) ]  =  4·ln(6) - ln(3)

--->  x  =  [ 4·ln(6) - ln(3) ] / [ ln(3) + ln(6) ]

geno3141 Apr 12, 2015
 #2
avatar+109721 
+10

 

 

$$\\3^{x+1}=6^{4-x}\\\\
ln[3^{x+1}]=ln[6^{4-x}]\\\\
(x+1)ln3=(4-x)ln6\\\\
xln3+ln3=4ln6-xln6\\\\
xln3+xln6=ln6^4-ln3\\\\
x(ln3+ln6)=ln1296-ln3\\\\
xln18=ln432\\\\
x=\frac{ln432}{ln18}\\\\$$

 

This answer is identical to Geno's

 Apr 12, 2015

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