Exponential inqualities

Since 2^2x+1 and 3*2^x-2 are always positive ( negative power only means 1/itself)
so the inequality has no solution

y=2^x-1 is transformed one unit to the right from the original graph y = 2^x
so , the x- axis of y=2^x-1 is 0.5 but not 1 anymore
also, the graph tends to 0 when x tends to -ve infinity
therefore, the general shape of the graph: http://imageshack.us/a/img21/2830/screenhunter01oct231243.gif


y=8^(2x+3) - 5 = 64^(x+3/2) -5 which is transformed 3/2 units to the left and 5 units downward form the original graph y = 64^x

also,the x - axis of y=8^(2x+3) - 5 is 507 but not 1
and it tends to -5 when x tends to -ve infinity

therefore,the general shape of the graph: http://imageshack.us/a/img842/4269/screenhunter02oct231253.gif

The graph of y = 2^x is always positive for all real values of x. So there is no solution for the inequality.