Question

Find the integer $n$ such that\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{0.001}}.\] Please help :(

Answer 1

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:

$\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{0.001}}.\]$

This can be further expressed as:

$\[10^n = 10^{3}\sqrt{\dfrac{10^{31}}{10^{-3}}}.\\\[10^n = 10^{3}\sqrt{10^{34}\\10^n = 10^3\cdot 10^{17}$

Since the use are equal, add the exponents

$10^n= 10^{3+17}\\10^n=10^{20}\\n=20$

Hence the value of n is 20 from the given indices

Learn more on indices here: brainly.com/question/10339517