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Basic of Logarithms
easy
If ${a^{1/x}} = {b^{1/y}} = {c^{1/z}}$ and ${b^2} = ac$ then $x + z = $
A
$y$
B
$2y$
C
$2xyz$
D
None of these
Solution
(b) ${a^{1/x}} = {b^{1/y}} = {c^{1/z}} = k\,({\rm{say}}) \Rightarrow a = {k^x},\,b = {k^y},\,c = {k^z}$
${b^2} = ac \Rightarrow {({k^y})^2} = {k^x}.{k^z}$ $ \Rightarrow $ ${k^{2y}} = {k^{x + z}} \Rightarrow x + z = 2y$.
Standard 11
Mathematics
