# Logrithmic question

#### jaypee

I'm having a hard time solving this:
e^(x+3) = pi^x

I got these results, but I'm not sure if it is correct:
ln^(x+3) = ln(pi^x)
(x+3)ln = xln(pi)
xln + 3ln = xln(pi)
3ln = xln(pi)-xln
3ln = x(ln(pi) - ln)

x = 3ln/ln(pi)-ln

NOTE: PI =3.14 (I don't know how to insert the symbol pi)

#### damgo

That's the right way to go about, but remember, ln is a function... you have to write ln(something), ln by itself is not a number.

ln(e)=1

and you should be able to get it from there...

#### chroot

Staff Emeritus
Gold Member
Yeah, you're kinda butchering things with your "ln raised to a power" and "ln by itself" stuff.

Step 1. Take the natural logarithm of both sides of the equation:

ln(e^(x+3)) = ln(pi^x)

this becomes

x+3 = x * ln(pi)

Step 2. Isolate x on one side of the equation

3 = x * ln(pi) - x
3 = x (ln(pi) - 1)

Step 3. Solve for x

x = 3 / (ln(pi) - 1)

- Warren

#### camel2

I'm having difficulty in solving for x,in the equation e^x=4-x^2
lne^x=ln(4-x^2)
x=ln(4-x^2) and this is as far as iI got

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