I apologize if this is a poorly formatted question, but i really need some help here…
I am trying to solve the following problem: $4\ln^3$
When I input this into my calculator, I get $4.3944$. However, when i input it into mathway, I get $5.0136$, which is the correct answer. Here is a picture of it in mathway: mathway_img
I have spent the last $2$ hours trying to figure out how to properly convert this problem into decimal form, as well as why my calculator keeps giving me a different answer. But, since I am new to logarithms, I have not been able to figure out how to get the answer $5.0136$.
Could someone please tell me how mathway gets this answer? Also, why does my calculator give me a different answer than mathway? Am I inputting it incorrectly?
Best Answer
The expression in question is
$$\frac{4\ln^3(11)}{11}\;.$$
In this context $\ln^3(11)$ means $(\ln 11)^3$, just as $\sin^2\theta$ normally means $(\sin\theta)^2$; this is approximately $2.3978953^3$, or about $13.787662$. Now multiply that by $4$ and divide by $11$ to get about $5.0136953$.