The main concept for this decibel problem is that the unknown, I, intensity, is under the control of the log function. Please read until the end of this paragraph. Then if this explanation isn't clear look up "functions and inverse functions" in a PreCalculus textbook, or look at the Khan academy video on inverse functions. The effect of a function can be canceled by applying its inverse function to the function. e.g. Suppose some function is acting on, or in control of, the number 7. If you apply the inverse of the function to the function acting on 7, the result is 7. In order to remove I, intensity, from the control of the log function we must apply the inverse function of the log function, which is 10 raised to a power. e.g. 10^( log(7) ) evaluates to 7. Note that the inverse function must be applied to both sides of the equation. In this problem, both sides of the decibel formula become the power of the base 10.
Use a calculator that has a 10^x function key. Use -3.8 for the x value and the calculator will give a result of 1.585 x 10^-4. Or, Change 10^(-3.8) to 10(+0.2) times 10^(-4). Use a calculator to evaluate 10 (+0.2) which yields 1.585. Now you have 1.585 times 10^(-4).
