SOLUTION: Solve the following equations by expressing each side as a power of the same base and then equating exponents: 4^(3x+5)=1/256 and 4^(x+10)=8^(x-6)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve the following equations by expressing each side as a power of the same base and then equating exponents: 4^(3x+5)=1/256 and 4^(x+10)=8^(x-6)      Log On


   

Question 269060: Solve the following equations by expressing each side as a power of the same base and then equating exponents:
4^(3x+5)=1/256

and
4^(x+10)=8^(x-6)
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4^(3x+5)=1/256
4%5E%283x%2B5%29+=+4%5E-4
3x+5 = -4
x = -3
--------
and
4^(x+10)=8^(x-6)
Change to base 2
2^(2x+20) = 2^(3x-18)
You can finish it.