Question

Exponential Equations help?
Determine the exact value of x:
(1/8)^(x-3) = 2 * 16^(2x+1)

Answer 1

Are you using logarithms to solve?

Answer 2

can it be solved without logarithms??

Answer 3

I don't know how to solve w/o logs

Answer 4

okay...logarithms are fine then :)

Answer 5

Haha :)

First, take the log of both sides

Answer 6

Then apply your log rules...in other words......

Answer 7

\[\log (1/8)^{x-3}= (x-3) \log (1/8)\]

Answer 8

and \[\log (2 * 16^{2x +1}) = \log 2 + \log 16^{2x+1}\]

Answer 9

this equals \[\log 2 + (2x+1) \log 16\]

Answer 10

so now you have\[(x-3) \log (1/8)= \log 2 + (2x + 1) \log 16\]

Answer 11

evaluate the logs and solve the equation for x

Answer 12

There may be another way to solve, but I'm not sure

Answer 13

thanks :) ..but can you explain what you mean by evaluate the logs? i've never done them before, really. :S

Answer 14

ok, forget all that....i just figured out a better way :)

Answer 15

lol okay

Answer 16

1/8 = \[2^{-3}\]

Answer 17

and 16 = \[2^{4}\]

Answer 18

This gives you \[2^{-3(x-3)}= 2^{1}*2^{4(2x+1)}\]

Answer 19

For the exponents, use distributive property

Answer 20

\[2^{-3x+9}= 2^{1}*2^{8x +1}\]

Answer 21

on the right side, you can combine those by adding expontents

Answer 22

\[2^{-3x+9}=2^{8x+2}\]

Answer 23

Now, since the bases are equal, this means the exonents are =, so\[-3x + 9 = 8x + 2\]

Answer 24

Then, solve the equation for x

Answer 25

haha....that was easier than logs :)

Answer 26

yay! this makes so much sense to me. thanks so much :)

Answer 27

You're very welcome!