Question

Help solve 2^(1-2x)=3?

Answer 1

I'm learning of logs and functions :) I'm not quite sure where to go about solving this though :c

Answer 2

It looks like this:
\[2^{(1-2x)=3}\]
What you need to do, is solve the exponent like an equation, then substitute in, and solve.

Answer 3

=3 isn't in the exponent, is that alright?

Answer 4

@ParthKohli Help D:

Answer 5

Your main goal is to get the \(1 - 2x\) out of the exponent so you're able to solve the equation. Do you know that you can take the log of both the sides? Try doing that and see what you get.

Answer 6

Let's solve the exponent:
\[(1-2x)=3\]
\[2x = 4\]
\[x = 4\]
Now substitute in.
\[(1-2[4])=3\]
\[(1-8)=3\]
-7 = 3
Now...
\[2^{-7}\]
Can you solve from there?

Answer 7

I'm afraid that's not correct, @AnyTipzWouldHelp

Answer 8

I messed up, sorry.

Answer 9

it has a log base of 2

Answer 10

Am I supposed to have (1-2x) log 2 = log 3

Answer 11

Yes, very good. Now get the \(x\) alone.

Answer 12

The first step would be to divide both the sides by \(\log(2)\)

Answer 13

So (1-2x)=log3/log2?

Answer 14

Or no?

Answer 15

@ParthKohli

Answer 16

Yes. Or \(1 - 2 x = \log_2 3\).

Answer 17

Then what :)

Answer 18

Just "isolate" \(x\). For example, subtract 1 from both sides.

Answer 19

My answer options are :
x = 0.396
x = -0.396
x = -0.631
x = 0.631
Just to make sure we're going down the right track

Answer 20

3/2-1? This would equal .5

Answer 21

We very much are.

Answer 22

No, that will become \(-2x = \log_2(3) - 1\).

Answer 23

Alright, so don't literally solve it, but show the subtraction

Answer 24

Yes. What's the value of \(\log_{2}3\) according to your calculator?

Answer 25

How should I enter it? Just as log(2)3?

Answer 26

When I do that, I get .903089987

Answer 27

Have you heard the base-change property?

Answer 28

heard about*

Answer 29

I'm familiar with it, I could use a refresher

Answer 30

It just says that\[\log_a b = \dfrac{\log b}{\log a}\]

Answer 31

alright, I got 1.584962501 :)

Answer 32

Nice. Now just solve for \(x\).

Answer 33

Do I need to subtract one from this first? And then divide by negative two?

Answer 34

I got -.2924812505, is this correct @ParthKohli

Answer 35

Seems good. :)

Answer 36

Doesn't seem to be one of the choices. I wonder why.

Answer 37

LOL! I see that I accidentally wrote the wrong ones.. I chose answer choice -.292 :)

Answer 38

Right.