Mathematical Expression Simplification: (a^u)(1/ln a) + c = 13.5416

(a^u)(1/ln . a) + c

In the expression (a^u)(1/ln a) + c, we have a few different components: a, u, ln a, and c

In the expression (a^u)(1/ln a) + c, we have a few different components: a, u, ln a, and c.

First, let’s understand the individual terms:

– “a” represents a base number. This can be any positive number except for 1, since logarithm of 1 is undefined.
– “u” represents an exponent that is being used to raise “a” to a power.
– “ln a” is the natural logarithm of “a”. The natural logarithm, denoted as “ln”, is the logarithm with base e, where e is a mathematical constant approximately equal to 2.71828.
– “c” represents a constant term, which is typically added or subtracted in mathematical equations.

The calculation can be broken down step by step as follows:

1. Calculate a^u by raising the base “a” to the power of “u”.

Example: If a = 2 and u = 3, then a^u = 2^3 = 8.

2. Calculate ln a using the natural logarithm function.

Example: If a = 2, then ln a = ln(2) ≈ 0.69315.

3. Calculate (1/ln a) by taking the reciprocal of ln a.

Example: If ln a ≈ 0.69315, then (1/ln a) = 1/0.69315 ≈ 1.4427.

4. Multiply a^u by (1/ln a).

Example: If a^u = 8 and (1/ln a) ≈ 1.4427, then (a^u)(1/ln a) = 8 * 1.4427 ≈ 11.5416.

5. Finally, add the constant term “c” to the result.

Example: If c = 2, then (a^u)(1/ln a) + c = 11.5416 + 2 = 13.5416.

Therefore, the simplified expression for (a^u)(1/ln a) + c is 13.5416.

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