Posted by **Semja** on Tuesday, December 13, 2011 at 4:47pm.

How do I approach the following problem. Please don't give answer but just guidance as to how to approach these in general. I need to be able to solve without a calculator.

3^(2x+1)-16(3^x)+5=0

- Math - Exponentials -
**bonita**, Tuesday, December 13, 2011 at 5:07pm
Distribute

- Math - Exponentials -
**Semja**, Tuesday, December 13, 2011 at 5:16pm
Eventually answered my own question. No idea what distributing has to do with anything though...

I simplified 3^(2x+1) to ((3^x)^2)*3^x then substituted a variable for 3^x and solved the corresponding quadratic. Seems to have worked

- Math - Exponentials -
**Reiny**, Tuesday, December 13, 2011 at 6:18pm
I think you were on the right track, except

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

so let y = 3^x to change your equation to

3y^2 - 16y + 5 = 0

(y - 5)(3y - 1) = 0

y = 5 or y = 1/3

so 3^x = 5 or 3^x = 1/3

This cannot be solved WITHOUT a calculator

3^x = 5

log 3^x = log 5

x log3 = log 5

x = log5/log3 = appr. 1.465

but 3^x = 1/3

3^x = 3^-1

x = -1

so x = -1 or x = appr. 1.465

both answers verify in the original

## Answer this Question

## Related Questions

- General Chemistry - According to the following reaction, how many moles of Fe(OH...
- Math subject Calculus - Hi there I am having some difficulties to solve this ...
- health care 220 - can someone just tell me how to do this I can not get a hold ...
- HCA 220 - I need help with an assignment that is due today and I am totally lost...
- Statistics - The weather forecaster reports that the probability of rain ...
- Math - Is it possible to bend a 20cm length of wire into the shape of a ...
- math concepts - Matthew sits at his desk unable to figure out the answer to a ...
- Math - Hi,I need to know how to do question like this without using a calculator...
- Science - You are a Chemical engineer, trying to synthesize N2H4(l). Your boss ...
- IT210 - When building a house, a structured, modular approach is better than a ...