#1**+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