SOLUTION: I really don't even know where to begin with this problem. Let 2^a = 5 and 2^b = 7. Using exponent rules, solve the equation in terms of a and b. 0.4^x=343

Question 286256: I really don't even know where to begin with this problem.
Let 2^a = 5 and 2^b = 7. Using exponent rules, solve the equation in terms of a and b.
0.4^x=343
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Let 2^a = 5 and 2^b = 7. Using exponent rules, solve the equation in terms of a and b.
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0.4^x=343
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0.4 = 2/5 = 2/2^a = 2^(1-a)
343 = 7^3 = 2^3b
--> (2^(1-a))^x = 2^3b
x(1-a)) = 3b
x = 3b/(1-a)
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Let 2^a = 5 and 2^b = 7. Using exponent rules, solve the equation in terms of a and b.
0.4^x=343
[2^2/2*5]^x = 7^3
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Rewrite in terms of a and b:
(2^2/(2*2^a))^x = (2^b)^3
(2^2/2(a+1))^x = 2^(3b)
(2^(1-a))^x = 2^(3b)
(2^(x(1-a)) = 2^3b
-----------------------
Equate the exponents and solve for "x":
x(1-a) = 3b
x = (3b)/(1-a)
===================
Cheers,
Stan H.
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