Solve each exponential equation below. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.

(1) 3^(2x) + 3^(x) - 2 = 0

(2) 2^(x + 1) = 5^(1 - 2x)

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- August 9th 2008, 06:43 AMmagentaritaExponential Equations
Solve each exponential equation below. Express irrational solutions in exact form and as a decimal rounded to 3 decimal places.

(1) 3^(2x) + 3^(x) - 2 = 0

(2) 2^(x + 1) = 5^(1 - 2x)

- August 9th 2008, 09:08 AMthelostchild
for the first write it as

then set substitute in then solve the quadratic to find u then use the substitution and logs to find x - August 9th 2008, 01:43 PMmagentaritaEasy reply
You said to let u = 3^(x). Of course, I can select any letter of choice to represent 3^(x), right?

- August 9th 2008, 02:26 PMthelostchild
- August 9th 2008, 02:27 PMmasters
- August 9th 2008, 07:29 PMSoroban
Hello, magentarita!

There are a number of ways to solve #2 . . .

Quote:

Solve the following equation. Express irrational solutions

in exact form and as a decimal rounded to 3 decimal places.

We have: .

. .

Take logs: .

. . Therefore: .

- August 10th 2008, 06:20 AMmagentaritaThanks to all...Soroban
Thank you all. Soroban....I have seen you in other math forums.

Your name is familiar.