How do I solve the equation e^(x+3) = pi^x?

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In summary, the conversation discusses the process of solving the equation e^(x+3) = pi^x. The summary includes taking the natural logarithm of both sides, isolating x, and solving for x. The final solution is x = 3 / (ln(pi) - 1). The conversation also briefly touches on solving for x in the equation e^x = 4-x^2, but the solution is not fully determined.
  • #1

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)
 
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  • #2
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...
 
  • #3
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
 
  • #4
I'm having difficulty in solving for x,in the equation e^x=4-x^2
help please
lne^x=ln(4-x^2)
x=ln(4-x^2) and this is as far as iI got
 
Last edited:

1. What is a logarithm?

A logarithm is the inverse operation of exponentiation. It is used to solve for the exponent in an exponential equation.

2. How is a logarithm written?

A logarithm is typically written as logb(x), where b is the base and x is the argument. For example, log2(8) is the logarithm with a base of 2 and an argument of 8.

3. What is the relationship between logarithms and exponents?

The logarithm tells us what exponent is needed to raise the base to get a certain number. For example, log2(8) = 3 because 2 raised to the power of 3 is equal to 8.

4. What are the properties of logarithms?

There are several properties of logarithms, including the power property (logb(xm) = m * logb(x)), the product property (logb(xy) = logb(x) + logb(y)), and the quotient property (logb(x/y) = logb(x) - logb(y)).

5. How can logarithms be used in science?

Logarithms are commonly used in science to represent data that spans a large range of values. They are also used to solve exponential equations and model exponential growth and decay in various scientific fields such as biology, physics, and chemistry.

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