Question 1 Write In Logarithmic Form: 43, 64, A³, Log 4, 64,

Question 1write In Logarithmic Form43 64a3 Log 4 64b64 Log 4 3

Write in logarithmic form 43 = 64 A. 3 = log 4 64 B. 64 = log 4 3 C. 3 = log 64 4 D. 4 = log 3 64

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The given problem involves converting exponential equations into their equivalent logarithmic forms. To understand this process, recall that for any positive numbers a, b, and c, the exponential form a^b = c is equivalent to the logarithmic form log_a c = b. This means that logarithms express the power to which a base must be raised to produce a given number.

In the specific question, the exponential equation is 43 = 64. To express this in logarithmic form, identify the base and the argument. Since the base has not been explicitly provided, it is customary to assume the base as 4, given the options. Therefore, the exponential expression becomes 4^3 = 64. Using the logarithmic conversion rule, this translates to log_4 64 = 3.

Analyzing the options:

  • A. 3 = log 4 64 — This correctly represents the logarithmic form of 4^3 = 64, but note the notation lacks the base subscript.
  • B. 64 = log 4 3 — Incorrect; this reverses the relationship.
  • C. 3 = log 64 4 — Incorrect; logs are written with the base as a subordinate, not as the argument.
  • D. 4 = log 3 64 — Incorrect; no such relationship here.

The correct representation among the options is A, which corresponds to log_4 64 = 3. This accurately expresses the exponential equation in logarithmic form, confirming option A as the correct answer.

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