Find the complete solution set 163x 1 1327 2x Find the com

Find the complete solution set: 16^3x - 1 = 1/32^7 -2x Find the complete solution set for this equation: Squareroot log (2x - 7) = 2 Solve the equation Y = T + 3 log (1/4 x -13) for the variable X.

Solution

16^(3x-1)=1/32^(7-2x)

16=2^4     and 32=2^5

2^4(3x-1)= 2^-5(7-2x)

4(3x-1)= -5(7-2x)

12x-4= -35 +10x => 2x= -31 => x=-31/2

2) sqrt(log(2x-7))=2

log(2x-7)=4

2x-7=10^4

2x= 10007

x=10007/2