Question

clarify, critique, correct
how are the equations 2^7 = 218 and log₂(218) = 7 related?

• to answer the question above, yulissa says:

oi know that 2^x and log₂x are inverses, so all the numbers in the equations are the same.

• what do you think yulissa means?

Explanation:

Yulissa means that because the exponential function $2^x$ and the logarithmic function $\log_2x$ are inverse - functions of each other, the numbers involved in the exponential equation $2^7 = 218$ (which is incorrect as $2^7=128$) and its corresponding logarithmic equation $\log_2(218)=7$ (also incorrect as $\log_2(128) = 7$) should be the same in a sense related to the inverse - relationship. In inverse functions, if $y = f(x)$ and $x = f^{-1}(y)$, the input and output values are swapped. Here, in the exponential form the base is 2, the exponent is 7 and the result is supposed to be 128, and in the logarithmic form with base 2, the result of the exponential (the argument of the logarithm) and the exponent in the exponential swap roles.

Answer:

Yulissa is referring to the inverse - relationship between exponential and logarithmic functions, where the values in the two equations are related by the property of inverse functions.