Solve Logarithm Overkill: Find ln(ln[e^{e^{5}}])

  • Thread starter danielle36
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    Logarithm
In summary, the problem is to find the exact value of ln(ln[e^{e^{5}}]). The solution involves using the property that when the base of the exponent and log are the same, they cancel out. The final answer is 5. However, it is important to not simply post the answer and instead give helpful hints.
  • #1
danielle36
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[SOLVED] Logarithm overkill!

Hello again!
I have been working on this log, and the longer I work on it, the more confused I get! Here's the problem:
Find the exact value for:

[tex]ln(ln[e^{e^{5}}[/tex]])

----
Here's what I've tried so far:

[tex]e(ln[e^{e^5}}[/tex]])

[tex]e^{x} = ln(e^{e^5}}) [/tex]
[tex]e^{x} = e^{e^5}}[/tex]
[tex]e^{5} = (2.72)^{5}[/tex]
[tex]e^{x} = e^{149}[/tex]
[tex]x = 149 [/tex]

...I have no idea if I'm doing this right, but I'm not feeling like I am...Help?
 
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  • #2
are you trying to do two logs then two e's or one e then a log then two e's
very confusing!
 
  • #3
You have to use one of the properties of logs. When the bases of the exponent and log are same, they cancel.
 
  • #4
Hint: the answer is an integer.
 
  • #5
ln e ^x =x
Can you take it from there?
 
  • #6
i think the answer is 5 since ln and e cancaled out!
 
  • #7
hey thanks everyone! i was able to figure it out from there you guys are always a big help :)
 
  • #8
tramtran111 said:
i think the answer is 5 since ln and e cancaled out!

This is true
 
  • #9
tramtran111 said:
i think the answer is 5 since ln and e cancaled out!

NEVER post the answer just like that!
 
  • #10
malawi_glenn said:
NEVER post the answer just like that!

haha, I guess a perfect hint would be

[tex] lne^x=x[/tex]
 

1. What is a logarithm?

A logarithm is a mathematical function that represents the power to which a base number must be raised to produce a given number. It is the inverse function of exponentiation.

2. How do you solve logarithms?

To solve a logarithm, you need to isolate the variable inside the logarithm and then use the properties of logarithms to simplify the expression. This may involve using the product, quotient, or power rule of logarithms.

3. What is ln?

ln is the natural logarithm, which uses the base e (approximately equal to 2.718) instead of the commonly used base 10. It represents the logarithm of a number with respect to e.

4. What is the difference between ln and log?

The only difference between ln and log is the base used in their calculations. ln uses the base e, while log typically uses the base 10. However, some calculators or computer programs may have the option to use different bases for logarithms.

5. Can you provide an example of solving a logarithm?

Sure! Let's solve the logarithm ln(10x) = 3. We can rewrite this as e^3 = 10x, and then solve for x by dividing both sides by 10: x = e^3/10. So the solution to this logarithm is x = e^3/10.

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