How do you solve #2(5^(6x))-9(5^(4x))+13(5^(2x))-6 = 0#?

1 Answer
dani83
Aug 14, 2015

# x = 0 " or " x = 1/2log_5 2" or " x = 1/2log_5 (3/2) #

Explanation:

# 2(5^(6x))-9(5^(4x))+13(5^(2x))-6 = 0 #

Take # y = 5^(2x) #

# 2y^3-9y^2+13y-6 = 0 #
# (y-1)(y-2)(2y-3) = 0 #

# 5^(2x) = 1 " or " 5^(2x) = 2" or " 5^(2x) = 3/2 #
# x = 0 " or " x = 1/2log_5 2" or " x = 1/2log_5 (3/2) #

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