Question

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

I've simplified the problem from 8^(x-1) = 1/64 down to the problem which you see above, and I don't know what further step to take. I've been working with logs in this chapter

Answer 1

Take log on both sides

Answer 2

Log a^x =x loga

Answer 3

there are two ways to do this. the first way will help you understand logs. the second way is what @AravindG said. Think this way: 2 to the power of what equals 1?

Answer 4

I can't just get that, and what you both are hinting at sounds familiar, but I'm still unsure what to do. If I take the logs of both sides, would it look like this:
2 log(3x+3) = log (1) ?

Answer 5

your 2 and 3x+3 are switched

Answer 6

Ah, but is the right side of my equation correct? and do I just simplify from there?

Answer 7

yes.

Answer 8

so after I simplify log(2), do I multiply it by the
three or do I add it?

Answer 9

might want to show your work; not sure i can follow

Answer 10

Log a^x =x loga

Answer 11

3x + 3 log (2) = log(1)
3x + 3 * 0.301 = 0

Answer 12

is that how I should go about it?

Answer 13

well, you're missing some parenthesis. Let's not simplify the log of 2, rather, recognize that the logarithm of 1 in any base is always 0... (why is this? isn't a^0 always equal to 1)?...

Answer 14

I did that on the right side, I don't know what to do for the left side. How do I address the log of two in relation to the rest of the right side

Answer 15

(3x + 3)log (2) = log(1)
(3x + 3)log (2) = 0
log of 2 is just a number. let's divide both sides by log(2) and then by 3... what do we get?

Answer 16

wouldn't I just be left with 3x+3 = 0 then?

Answer 17

well, if you didn't divide by 3... either way you can solve for x I am sure now ;)

Answer 18

Ah, thanks!

Answer 19

No problem - advice for these problems, always check your answer(s) to make sure they satisfy the original equation, because you can get extraneous solutions... in this case you won't, but just be careful

Answer 20

Okie dokie