## Switching between exponential and logarithmic form

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.
 Recognitions: Homework Help $$5^{f(x)} = 5^{\log_5 x +3} = 5^{\log_5 x} \cdot 5^3 =125x$$
 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.

## Switching between exponential and logarithmic form

Can anyone explain this please? Or atleast tell me what to google to find out why this works?
 Recognitions: Homework Help 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 $$a^ma^n=a^{m+n}$$ on the 5^(log_5 x +3 ) and there we go :) And you trying to make it equal x? $$5^3x=5^{f(x)}$$ $$x=5^{f(x)-3}$$
 Ahh, alright, thank you very much Sir :)
 Recognitions: Homework Help Thats alright, but please don't call me sir. im 15 years old lol, Sir makes me feel like im 40 >.<" EDIT: Not that theres anything wrong with being 40 !!!:P EDIT 2: ..OR OLDER...damn political correctness..
 Could you tell me how you came up with 125x? P.S.:haha
 Recognitions: Homework Help $$5^{f(x)} = 5^{\log_5 x +3} = 5^{\log_5 x} \cdot 5^3$$. You should be able to follow that so far. Now, by definiton of the logaritim, $$a^{\log_a x} =x$$. And 5^3 is just 125 by expanding it..
 Okay, thanks a bunch:)

 Quote by wScott Could you tell me how you came up with 125x? P.S.:haha
53=125

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EDIT: I guess Gib Z beat me to it.
 Recognitions: Homework Help Lol just 16 minutes late d_leet :P

 Quote by Gib Z Lol just 16 minutes late d_leet :P
Eh, it's been a long day.
 Recognitions: Gold Member Science Advisor Staff Emeritus loga(x) and ax are inverse functions. If y= loga(x) then x= ay and vice-versa.
 here you go with graph > http://img123.imageshack.us/img123/6964/untitledfy8.jpg ps: the graph would be something like that but not exactly .