Part 1Change the logarithmic expression to an equivalent expression involving an exponentlog Subscript 2 Baseline left parenthesis one fourth right parenthesis equals negative 2log214=−2 Part 1The logarithm log Subscript 2 Baseline left parenthesis one fourth right parenthesis equals negative 2log214=−2 written as an exponential equation is [input]enter your response here .(Type an equation. Use integers or fractions for any numbers in the equation.)

Question

Part 1Change the logarithmic expression to an equivalent expression involving an exponentlog Subscript 2 Baseline left parenthesis one fourth right parenthesis equals negative 2log214=−2 Part 1The logarithm log Subscript 2 Baseline left parenthesis one fourth right parenthesis equals negative 2log214=−2 written as an exponential equation is [input]enter your response here .​(Type an equation. Use integers or fractions for any numbers in the​ equation.)

BlackTom AI · Accepted Answer

We start by restating the given situation: a logarithmic expression log base 2 of 1/4 equals -2, and we are asked to write its exponential form.
Since log₂(1/4) = -2, by the definition of logarithms, this means that 2 raised to the power of -2 equals 1/4. In other words, the exponential form is 2^(-2) = 1/4.
To check the accuracy, recall that the logarithmic statement log_b(a) = c is equivalent to the exponential statement b^c = a. Applying this with b = 2, a = 1/4, c = -2 confirms the equivalence: 2^(-2) = 1/4.
Understanding this, the single correct exponential form is the equation where the base matches the logarithm's base (2), the exponent is the value of the logarithm (-2), and the result is the argument of the logarithm (1/4).
If one explores alternatives, any change to the base, exponent, or result would violate the fundamental log-to-expo conversion rule, leading to an incorrect equality.
In summary, converting log₂(1/4) = -2 into exponential form yields 2^(-2) = 1/4, which aligns perfectly with the core relationship between logarithms and exponents.

类似问题

Select the value that is equal to ⌊log229⌋.

Solve each of the following equations for . log 4 64 = x, 𝑙 𝑜 𝑔 4 1 256 = x

Use the properties of logarithms to find the exact value of the expression. Do not use a calculator.

Simplify Change the logarithmic statement to an equivalent statement involving only one logarithm. log3(x)−8 log3(x+8)

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Use the properties of logarithms to find the exact value of the expression. Do not use a calculator. log 3 ⁡ 24 − log 3 ⁡ 8

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ln(A x B x C) equals

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