Mathematics

Prove the following:
27^{log 2} = 8^{log 3}

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Given,

27^{log 2} = 8^{log 3}

Taking log on both sides we get,

⇒ log 27^{log 2} = log 8^{log 3}

⇒ log 2.log 27 = log 3.log 8

⇒ log 2.log 3³ = log 3.log 2³

⇒ 3.log 2.log 3 = 3log 3.log 2

Since, L.H.S. = R.H.S. hence proved,

Hence, proved that 27^{log 2} = 8^{log 3}.

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