Answer:
c=ab/(2b+a)
Step-by-step explanation:
20^c = 4^c * 5^c
20^c= (2^2)^c * 5^c
20^c= (2 )^(2c) * ( 5 )^c
Raise both sides to power a
20^(ca)=(2^a)^(2c) * (5 )^(ac)
20^(ca)=(20^c)^(2c) * (5 )^(ac)
Raise both sides to power b
20^(cab)=(20)^(2c^2b)*(5^b)^(ac)
20^(cab)=20^(2c^2b) * (20^c)^(ac)
20^(cab)=20^(2c^2b) * 20^(ac^2)
Rewriting using law of exponents on right hand side
20^(cab)=20^(2c^2b+ac^2)
Now bases are same so that means the exponents have to be the same, that is we have:
cab=2c^2b+ac^2
assuming c is not 0, divide by c on both sides
ab=2cb+ac
Factor the right hand side
ab=c(2b+a)
Divide both sides by (2b+a)
c=ab/(2b+a)
