2

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?

Moist Carrot
  • 23
  • Given the image at the link, I find it hard to believe that your input to your calculator was actually $4\ln^3$, which should in fact not yield any numerical result; what did you actually input? – Brian M. Scott Jun 20 '20 at 02:05
  • @BrianM.Scott I put in 4ln(3) but i do not think that is the same as putting in 4ln^3. I have tried inputting it multiple ways but i still cannot seem to get the answer 5.0136. – Moist Carrot Jun 20 '20 at 02:08
  • 1
    You’re right: $4\ln 3$ is something completely different. But you’ve completely ignored part of the expression: what happened to the $11$ inside the logarithm and the $11$ in the denominator? – Brian M. Scott Jun 20 '20 at 02:11
  • What do you mean $4\ln ^3$? What does that mean? Did you mean $4 \ln(3)$ or $4\ln^3 (something)$ (if so what?). The phrase $4\ln^3$ doesn't mean anything. – fleablood Jun 20 '20 at 02:38
  • Why are you leaving out the $11$? That is an essential part of the problem. Are you assuming you can cancel things out from within the expression? For example would you think $\frac {2\sqrt{7}}{7} = {2\sqrt{{\ \ }}}$? But $2\sqrt{\ \ }$ is meaningless. So is $4\ln^3$ is meaningless. – fleablood Jun 20 '20 at 02:43

3 Answers3

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 $5.0136953$.

Brian M. Scott
  • 616,228
1

Input this into your calculator instead:

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

Benjamin Wang
  • 3,920
1

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.

slumpyrat
  • 11