Final answer:
The expression 'Log ^23 + log ^200 + log ^26' simplifies to 'log(119600)' by using the property of logarithms that allows us to combine logs when they are added. Logarithms can be added together by taking the logarithm of the product of the inside numbers if they are of the same base.
Step-by-step explanation:
The student wants to evaluate the expression Log ^23 + log ^200 + log ^26. This looks like a simplification problem involving logarithms in mathematics. From the question, we can assume that the logarithms are using base 10 as no other base is specified. According to the properties of logarithms, when you add logarithms together, it is equivalent to taking the logarithm of the product of the individual numbers inside each log function. This principle mirrors the exponent rule that states a·b = b + a when both are to the same base.
Using this property, we can combine the logarithms:
- log(23) + log(200) + log(26)
- log(23 × 200 × 26)
- log(119600)
Now we have a single logarithm, log(119600), which is the power you raise 10 to get 119600. There's no simpler exact form for this logarithm, but you can compute its value using a calculator. Therefore, the evaluated expression is the logarithm of 119600.
Additionally, we can illustrate with an example using the properties of the exponential and natural logarithm. If we had an expression like eln (x), we could simplify it to x, because 'e' is the base of the natural logarithm and 'ln' is the natural logarithm function, so they are inverses of each other.