The exponential equation, 24 = x, can also be written in which alternate logarithmic notation : log 2 x = 4

Question

The exponential equation, 24 = x, can also be written in which alternate logarithmic notation : log 2 x = 4

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We start by restating the core relationship: the exponential equation 24 = x can be expressed in logarithmic form. 
Option 1: 'log 2 x = 4' reads as the logarithm of x with base 2 equals 4, i.e., log base 2 of x equals 4. This is exactly equivalent to 2^4 = x, which simplifies to x = 16, which is not 24, so we need to check the intended base and exponent carefully. However, in standard notation, log base 2 of x equals 4 corresponds to x = 2^4 = 16, which would not match 24. This reveals a potential mismatch in interpreting the given exponential form; but if we interpret the expression as log base 2 of x equals 4, it represents the relationship 2^4 = x. Since 2^4 = 16, this would imply x = 16, not 24, so this option does not correctly represent 24 = x.
Option 2: 'log 4 x = 2' means log base 4 of x equals 2, i.e., 4^2 = x, giving x = 16. Again, this does not match x = 24, so this option is not equivalent to the original.
Option 3: 'log x 2 = 4' reads as log base x of 2 equals 4, which translates to x^4 = 2. That would produce x = 2^(1/4), a very different value from 24, so this is incorrect.
Option 4: 'log x 4 = 2' means log base x of 4 equals 2, i.e., x^2 = 4, so x = 2 (or -2, disregarding negative bases). This also does not match the original x = 24, so it is not equivalent.
Taken together, only one option directly expresses the exponential relationship 24 = x in logarithmic form using the natural base connection, and the remaining choices alter the base or the resulting value, leading to mismatches. The correct representation should equate to x = 2^4, i.e., a logarithm with base 2 yielding 4, but with the given options, the one that best aligns conceptually as log base 2 of x equals 4 is option 1, while recognizing that it would imply x = 16 under strict interpretation, which indicates a mismatch in the stated equivalence. The other options involve different bases or misunderstood log interpretations, producing values inconsistent with x = 24.

CO.BU.Quantitative_Business_Prep Module 1 Quiz

The exponential equation, 24 = x, can also be written in which alternate logarithmic notation : log 2 x = 4

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