Answer:
x = 11/2
Step-by-step explanation:
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The value of n is 20 from the given indices
<h3>How to determine the variable in an exponential function</h3>
Given the exponential function expressed as:
![\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{0.001}}.\]](https://tex.z-dn.net/?f=%5C%5B10%5En%20%3D%2010%5E%7B3%7D%5Csqrt%7B%5Cdfrac%7B10%5E%7B31%7D%7D%7B0.001%7D%7D.%5C%5D)
This can be further expressed as:

Since the use are equal, add the exponents

Hence the value of n is 20 from the given indices
Learn more on indices here: brainly.com/question/10339517
we are given
the least common multiple of 5, 9 and 30
we know that

so, firstly, we will find prime factorization






so,
LCM of 5 , 9 and 30 is 90........Answer