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Write 65=77766^{5}=7776 in logarithmic form\newline(A) log⁡65=7776\log_{6}5=7776\newline(B) log⁡67776=5\log_{6}7776=5\newline(C) log⁡56=7776\log_{5}6=7776\newline(D) log⁡57776=6\log_{5}7776=6

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Q. Write 65=77766^{5}=7776 in logarithmic form\newline(A) log⁡65=7776\log_{6}5=7776\newline(B) log⁡67776=5\log_{6}7776=5\newline(C) log⁡56=7776\log_{5}6=7776\newline(D) log⁡57776=6\log_{5}7776=6
  1. Understand Relationship: Understand the relationship between exponential and logarithmic forms. The exponential form by=xb^y = x can be rewritten in logarithmic form as log⁡b(x)=y\log_b(x) = y, where bb is the base, yy is the exponent, and xx is the result.
  2. Identify Values: Identify the base bb, exponent yy, and result xx in the given exponential equation.\newlineIn the equation 65=77766^{5}=7776, the base bb is 66, the exponent yy is 55, and the result xx is 77767776.
  3. Convert to Logarithmic Form: Convert the exponential equation to logarithmic form using the relationship from Step 11.\newlineUsing the identified values, the logarithmic form of the equation is log⁡6(7776)=5\log_6(7776) = 5.
  4. Match with Options: Match the converted logarithmic equation with the given options.\newlineThe correct logarithmic form is log⁡6(7776)=5\log_6(7776) = 5, which matches option (B)(B).

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