Question

Solve for x. 3 ^(2x+2) = 8

Answer 1

Im confused on how to solve this with 2x+2 being a exponent

Answer 2

\[\huge 3^{\color{royalblue}{2x+2}}=8\]
Hmm our X is in the exponent! That's no good.
So we'll have to apply some fancy work with logarithms.

Answer 3

Take the natural log of both sides.\[\huge \ln\left(3^{\color{royalblue}{2x+2}}\right)=\ln 8\]

Answer 4

An important rule of logarithms states,\[\huge \log (a^b)= b\cdot \log (a)\]We're going to apply this to our problem, giving us,\[\huge \color{royalblue}{(2x+2)}\ln(3)=\ln 8\]Understand what we did there? :o

Answer 5

so I do the In for 3 and 8?

Answer 6

We did the natural log of the entire left side, and the entire right side.
Then, using a rule of logarithms, we were able to bring the exponent down in front of the log.

Now we have just a little bit more work to solve for x.

Answer 7

Divide both sides by ln(3),\[\huge \color{royalblue}{2x+2}=\frac{\ln8}{\ln3}\]

Then we'll subtract 2 from each side,\[\huge \color{royalblue}{2x}=\frac{\ln8}{\ln3}-2\]
Then we'll divide both sides by 2,\[\huge \color{royalblue}{x}=\frac{\ln8}{2\ln3}-1\]

Answer 8

It's a bit of work to solve this one, getting confused on the logarithms?

Answer 9

I got rounded 0.14

Answer 10

is that correct and the more complicated ones Im confused with

Answer 11

Hmm I got -0.0536

Lemme try it again to make sure I didn't make a mistake.

Answer 12

Yah I'm still coming up with -0.0536.
Yah I checked it on wolfram, same answer.

Having a little trouble punching it in correctly on the calculator? :o

Answer 13

I guess so. im doing it on my omputer calculator. i did 8 in / 2*3 in = then subtract by one

Answer 14

Well I'm not sure what your computer calculator looks like.
But on a normal TI calculator it looks something like this.
\[\huge ((\ln(8))\div (2 \ln(3)))-1\]
I definitely prefer to do it in pieces instead of using this many parentheses.

Answer 15

Are you using the Windows Calculator?

Answer 16

For the Windows Calculator you would put it in like this,\[\huge 8 \ln\quad /\quad 2 \quad / \quad 3 \ln \qquad \text{Enter} \qquad - \quad 1\]