Switching between exponential and logarithmic form

In summary, the conversation discusses the process of converting a logarithmic equation into its exponential form and explains that the base of the logarithm is raised to the power of the expression inside the logarithm. The individual asking the question is curious about the reasoning behind this process and also inquires about finding an "x=" form of the equation. The conversation also touches on the inverse relationship between logarithmic and exponential functions and provides a graph to illustrate the concept.
  • #1
wScott
88
0
Hello you bunch of owls, I'm doing my homework at the moment and I'm curious, how woul I express the logarithmic equation

f(x) = log5 (x) + 3 in it's exponential form (where 5 is the base).

This isn't part of the homework, I'm just supposed to graph it, but I'm curious as to what the exponential form looks like.
 
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  • #2
[tex]5^{f(x)} = 5^{\log_5 x +3} = 5^{\log_5 x} \cdot 5^3
=125x[/tex]
 
  • #3
Umm, I'm sure you're right, but could you elaborate on why that's correct? Could you explain how you got that i mean.

And is there a x= form of that, that's what I'vebeen trying to come up with :p.
 
  • #4
Can anyone explain this please? Or atleast tell me what to google to find out why this works?
 
  • #5
Well say I have something equal to each other. a=b.

Then x^a is equal to x^b, since a=b. So in this case, f(x)=log_5 x + 3, I did
5^(log_5 x+3) = 5^(f(x)), and I reversed the rule [tex]a^ma^n=a^{m+n}[/tex] on the 5^(log_5 x +3 ) and there we go :)

And you trying to make it equal x?
[tex]5^3x=5^{f(x)}[/tex]
[tex]x=5^{f(x)-3}[/tex]
 
  • #6
Ahh, alright, thank you very much Sir :)
 
  • #7
Thats alright, but please don't call me sir. I am 15 years old lol, Sir makes me feel like I am 40 >.<"

EDIT: Not that there's anything wrong with being 40 !:P

EDIT 2: ..OR OLDER...damn political correctness..
 
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  • #8
Could you tell me how you came up with 125x?

P.S.:haha
 
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  • #9
[tex]5^{f(x)} = 5^{\log_5 x +3} = 5^{\log_5 x} \cdot 5^3
[/tex]. You should be able to follow that so far. Now, by definiton of the logaritim, [tex]a^{\log_a x} =x[/tex]. And 5^3 is just 125 by expanding it..
 
  • #10
Okay, thanks a bunch:)
 
  • #11
wScott said:
Could you tell me how you came up with 125x?

P.S.:haha

53=125

/*extra characters*/

EDIT: I guess Gib Z beat me to it.
 
  • #12
Lol just 16 minutes late d_leet :P
 
  • #13
Gib Z said:
Lol just 16 minutes late d_leet :P

Eh, it's been a long day.
 
  • #14
loga(x) and ax are inverse functions.
If y= loga(x) then x= ay and vice-versa.
 
  • #15
here you go with graph >

http://img123.imageshack.us/img123/6964/untitledfy8.jpg

ps: the graph would be something like that but not exactly .

:zzz:
 
Last edited by a moderator:

1. What is the basic concept behind switching between exponential and logarithmic form?

The basic concept is that exponential form represents repeated multiplication, while logarithmic form represents the exponent needed to obtain a certain value.

2. How do you convert from exponential to logarithmic form?

To convert from exponential to logarithmic form, use the base of the exponential as the base of the logarithm, and equate the exponent to the value in the logarithmic form. For example, 2^3 = 8 can be written as log base 2 of 8 = 3.

3. What is the relationship between exponential and logarithmic functions?

Exponential and logarithmic functions are inverses of each other. This means that if we evaluate an exponential function at a certain value, we can use the logarithmic function with the same base to find the exponent needed to obtain that value.

4. When would you need to switch between exponential and logarithmic form in real-world applications?

Exponential and logarithmic functions are commonly used in fields such as finance, biology, and physics. They can be used to model population growth, radioactive decay, and compound interest, among other things.

5. What are some tips for effectively switching between exponential and logarithmic form?

One tip is to remember that the exponent in the exponential form becomes the value in the logarithmic form, and vice versa. Additionally, keeping track of the base of the exponential or logarithmic function can help with converting between the two forms.

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