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.

Assignment Viewer

查看解析

登录即可查看完整答案

类似问题

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)

Simplify Change the logarithmic statement to an equivalent statement involving only one logarithm. log 3 ⁡ ( 𝑥 ) − 8 log 3 ⁡ ( 𝑥 + 8 )

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

Solve the Equation Solve the following equation. Write the answer in terms of the natural logarithm. 𝑒 2 𝑥 = 9

ln(A x B x C) equals

An earthquake measured 3.1 on the Richter scale. How many times as intense as a standard earthquake was this one?

What is the magnitude of an earthquake 1410 times as intense as a standard earthquake?

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单