Question

x^a=c^b and x^c=c^a prove a^2=bc

Answer 1

x^a=c^b
x=c^b/a - 1
x^c=c^a
x=c^a/c - 2
from 1 and 2
c^b/a=c^a/c
bases are equal powers are also equal
b/a=a/c
cross multiplication
a^2=bc
hence proved

Answer 2

Hey there!

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Given,
${x}^{a} = {c}^{b} \\ x = ( {c}^{b} ) ^{ \frac{1}{a} } = {c}^{ \frac{b}{a}}.................................(1) \\ {x}^{c} = {c}^{a} \\ \\ ( {c}^{ \frac{b}{a} } )^{c} = {c}^{a} ...........................(from1) \\ \\ \frac{bc}{a} = a \\ \\ hence \\ \\ a^2 = bc$