SOLUTION: The substitution u=2^x can be used to convert the equation 4^x−2^(x+1)−15=0
to the form u^2+au+b=0
Ho2 do I find the value of a and b?
Algebra.Com
Question 1009860: The substitution u=2^x can be used to convert the equation 4^x−2^(x+1)−15=0
to the form u^2+au+b=0
Ho2 do I find the value of a and b?
Found 2 solutions by josmiceli, Boreal:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
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So, the equation is:
If this is the form to get it into:
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
u^2+au+b=0
u=2^x
4^x=2^2x=2^x*2^x=u^2
2^(x+1)=2^x*2=2u
u^2-2u-15=0
(u-5)((u+3)=0
u=5, -3, the -3 root is extraneous.
2^x=5
log both sides
xlog 2=log5
x= log 5/log2=2.3219
4^2.3219=25.00
2^3.3219=10
a=-2, b=-15
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