1. ## a^x=log_a_x

At what value of a will the graph of A^x and log base(a) of (x) equal eachother?

a^x=log_a_(x)?

what i said was either one will intercept with the line y=x (Because since a^x and log_a_(x) are inverses. they will intersect at the line y=x

so i made a^x=x, still couldnt solve

the same with log_a_(x)=x
Any ideas?

ps. i use latex and winedt. is there a sticky on how to write that code through here or it won't work?

cheers

2. ps. i use latex and winedt. is there a sticky on how to write that code through here or it won't work?
Yes, look at this thread: http://www.mathhelpforum.com/math-he...-tutorial.html .

a^x=log_a_(x)
you get
$\displaystyle a^x \;=\; \log_a x$

01

EDIT: completely misread the question...

3. Does the question place restrictions on $\displaystyle a$? Usually with logarithms, $\displaystyle a>1,$ in which case the functions will never intercept...

When you post, hit the button up on the toolbar that looks like a capital sigma. That will give you math tags. Type your LaTeX between these tags, and all will be well...

4. Originally Posted by sebko
At what value of a will the graph of A^x and log base(a) of (x) equal eachother?

a^x=log_a_(x)?

what i said was either one will intercept with the line y=x (Because since a^x and log_a_(x) are inverses. they will intersect at the line y=x

so i made a^x=x, still couldnt solve

the same with log_a_(x)=x
Any ideas?

ps. i use latex and winedt. is there a sticky on how to write that code through here or it won't work?

cheers
Consider the case that the graphs of $\displaystyle f: f(x)=a^x$ and $\displaystyle g: g(x)=\log_a(x)$ are tangent to each other.

Then the tangent point must be placed on the line $\displaystyle y=x$ and the gradient of both graphs must be 1 at the tangent point

$\displaystyle a^x=\log_a(x)~\wedge~a^x=x~\wedge~\ln(a)\cdot a^x=1$

Solve the 3rd equation for $\displaystyle a^x$ and plug in this term into the first equation. Solve for a and x.

I've got $\displaystyle a = \sqrt[e]{e}$

5. Restrictions i believe were a>1 and a<=2

6. Originally Posted by sebko
Restrictions i believe were a>1 and a<=2
My result fits miraculously into this interval:

$\displaystyle 1 < \sqrt[e]{e} \approx 1.44466786... \leq 2$

7. Thankyou so much earboth... with your help i solved it myself aswell!

I tried to put the LATEX that i did in here but i still wouldnt let me it said Syntax, even though i have latexd it with winedt , and saved it as a pdf with no errors... anyway. Here is my .tex file. and my .pdf

.tex file
problem.tex

.pdf file
problem.pdf