211) consider f(x) = 6x - 8x + 1 + 27x-1
at x= -∞ f(x)=1
also f is strictly increasing so no real root..
$(1) Solve the equation $6^x+27^{x-1} = 8^x-1.$
$(2) Solve the equation $5.2^x+4.3^x = 3.4^x+2.5^x$
$(3) Solve the equation $3^{x+1}-9^x+3.5^x-25^x=15^x+3$
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4 Answers
21212)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
213)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