Final answer:
The question seems to be related to finding the least integer for a math function involving logarithms and exponential expressions, but it contains typos that prevent a full solution. Logarithm properties and the relationship between exponential functions and natural logarithms are highlighted as essential tools in such problems.
Step-by-step explanation:
The question fragment appears to be asking for the least integer n for a math function, which seems related to logarithmic and exponential expressions. Unfortunately, the question is incomplete and has typos that prevent a clear understanding of the problem that needs to be solved. However, I can provide some general assistance on the topics mentioned in the fragments provided.
To find the least integer n for given conditions, we sometimes have to establish a relationship or an equation that must be satisfied by that integer. The reference to the logarithms implies that we're possibly dealing with a logarithmic function, where the base of the logarithm and its properties might be relevant. For example, the property loga(b) = loga(c) − loga(d) can simplify expressions and solve equations involving logarithms.
The fragments mention an exponential function and provide a trick for solving problems involving growth: representing numbers using the natural logarithm and the exponential function as inverse functions. This is useful for converting between logarithmic and exponential forms, such as expressing the number 2 as eln(2).
On to solving equations with both exponential and logarithmic parts, we use laws of logarithms and exponents to isolate variables and find the smallest integer that satisfies the equation. The mentioned math trick might be useful in such cases, where functions undo each other, easing the simplification process.