If a = c^z, b = a^x and c = b^y prove that xyz = 1.
Answers
a = c^z b = a^x c = b^y
10 can be written as 10 = 10^log 10
100 can be written as 100 = 10^log 100
a can be written as a = 10^log a
b can be written as b = 10^log b
c can be written as c = 10^log c
a = c^z
10^log a = ( 10^log c )^z
Bases are common for above two eqs
So exponents will be equal
log a =( log c)^z
log a = z log c
z = (log a) /(log c)
b = a^x
10^log b = ( 10^log a )^x
Bases are common for above two eqs
So exponents will be equal
log b =( log a)^x
log b = x log a
x = (log b) /(log a)
c = b^y
10^log c = ( 10^log b )^y
Bases are common for above two eqs
So exponents will be equal
log c =( log b)^y
log c = y log b
y = (log c) /(log b)
x*y = (log b/log a)*(log c /log b)
= (log b * log c)/(log a * log b)
= (log c) / (log a)
(x*y)*z =( log c / log a )*(log a / log c )
=(log c * log a )/(log a * log c)
= 1
xyz = 1