Question

if a power x = b power y and b power x = a power y (ab is unequal to 1) then prove that,a = b.​

Answer 1

Answer:

a^x=b^y=c^z

a^x=b^y\implies a=b^\frac{y}{x}----(1),

b^y=c^z\implies c=b^\frac{y}{z} -----(2),

We have,

b^2=ac

b^2=b^\frac{y}{x}.b^\frac{y}{z}

b^2=b^{\frac{y}{x}+\frac{y}{z}}              (a^m.a^n=a^{m+n})

2=\frac{y}{x}+\frac{y}{z}             (a^m=a^n\implies m=n)

2=\frac{y(z+x)}{xz}

\implies y=\frac{2xz}{x+z}

Hence, proved...

Answer 2

Answer:

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Step-by-step explanation:

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