The value of n is 20 from the given indices
How to determine the variable in an exponential function
Given the exponential function expressed as:
[tex]\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{0.001}}.\][/tex]
This can be further expressed as:
[tex]\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{10^{-3}}}.\\\[10^n = 10^{3}\sqrt{10^{34}\\10^n = 10^3\cdot 10^{17}[/tex]
Since the use are equal, add the exponents
[tex]10^n= 10^{3+17}\\10^n=10^{20}\\n=20[/tex]
Hence the value of n is 20 from the given indices
Learn more on indices here: https://brainly.com/question/10339517
