+0  
 
+5
128
1
avatar

Solve the equation 

2^(4 x + 16) = 6^(5 − 7 x)

Guest Mar 2, 2017
 #1
avatar
+5

Solve for x over the real numbers:
2^(4 x + 16) = 6^(5 - 7 x)

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(2) (4 x + 16) = log(6) (5 - 7 x)

Expand out terms of the left hand side:
4 log(2) x + 16 log(2) = log(6) (5 - 7 x)

Expand out terms of the right hand side:
4 log(2) x + 16 log(2) = 5 log(6) - 7 log(6) x

Subtract 16 log(2) - 7 x log(6) from both sides:
(4 log(2) + 7 log(6)) x = 5 log(6) - 16 log(2)

Divide both sides by 4 log(2) + 7 log(6):
Answer: |x = (5 log(6) - 16 log(2))/(4 log(2) + 7 log(6))  = - 0.139181898....

Guest Mar 2, 2017

5 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.