exponential equation.

1) consider f(x) = 6^x - 8^x + 1 + 27^x-1

at x= -∞ f(x)=1

also f is strictly increasing so no real root..

2)consider f(x)= 5(2)^x + 4(3)^x - 3(4)^x - 2(5)^x

clearly x=1 is a solution

for positive x, function is strictly decreasing

at x= -∞ f is zero ,for negative x ,function is strictly increasing

so only solution x=1

3)f(x)= (3)^(x+1) - (9)^x + 3(5)^x - (25)^x - (15)^x - 3

x=0 is a solution

at x= -∞ f(x)= -3

for negative x f is strictly increasing

for positive x f is strictly dereasing

x=0 only solution