Converting logarithm to decimal form

Question

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?

Answer 1

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 $5.0136953$.

Answer 2

Input this into your calculator instead:

$$\frac{4\times (\ln (11))^3}{11}.$$

Answer 3

You are most likely inputting it incorrectly into your calculator. The answer you are getting is due to the following input: $$4\cdot\ln(3)$$ which will give you 4.3944...

As others have noted already, try this instead. $$\dfrac{4\cdot(\ln(11))^{3}}{11}$$

Using the parenthesis above might clean up some of the confusion especially if it's an older style calculator.