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Problem: If

27^{x} = 81^{y}

, Find the value of

\frac{x}{y}

answer:

\frac{4}{3}

Problem: If

a^{a \sqrt{a}} = (a \sqrt{a})^{a}

, Find the value of a

answer:

\frac{9}{4}

Problem: If a+b+c=0 show that,

\frac{1}{x^{b} + x^{- c} + 1}

\frac{1}{x^{c} + x^{- a} + 1}

\frac{1}{x^{a} + x^{- b} + 1}

= 1.

Problem:

A = \frac{x y + z x - x^{2}}{\log_{k} x}, B = \frac{y z + x y - y^{2}}{\log_{k} y}, C = \frac{z x + y z - z^{2}}{\log_{k} z}

If A=B=C, then prove that,

x^{y} y^{x} = y^{z} z^{y} = z^{x} x^{z}

Solve Exponential Equations