+0  
 
+5
73
1
avatar

Solve the equation 

2^(4 x + 16) = 6^(5 − 7 x)

Guest Mar 2, 2017
Sort: 

1+0 Answers

 #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

11 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details