We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
390
2
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+17746 
+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+17746 
+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+100247 
+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

31 Online Users

avatar