what is 8/(3^x)=2^(x+2)?

Question

what are the steps or at least how would u go it without graphing

Answer 1

8/(3^x) = 2^(x + 2)

First multiply both sides by 3^x.

8 = [2^(x + 2)] [3^x]

Now, decompose 2^(x + 2) into (2^2)(2^x).

8 = [(2^2) (2^x)] [3^x]

Simplify.

8 = 4 (2^x)(3^x)

By an exponential property, (ab)^m = (a^m)(b^m), so we have

8 = 4 [(2)(3)]^x

Simplify

8 = 4(6^x)

Divide both sides by 4.

2 = 6^x

And now convert this to logarithmic form.

log[base 6](2) = x

If you want an approximation,

log[base 6](2) = ln(6)/ln(2) {Change of Base formula), so

x = ln(6)/ln(2) {in case you want to punch this into your calculator}

Answer 2

That equation has only one variable, so I don't think you can graph it. You might be trying to solve for x, though, and if that's the case, it might help to graph the function y = 8/(3^x) - 2^(x+2) on a graphing calculator and find where it crosses the x-axis...

But anyway, if you are in fact solving for x, you can actually get an exact answer without using a graphing calculator. First multiply both sides by 3^x to get

8 = (3^x)*(2^(x+2))

Rewrite 2^(x+2) as 2*2*(2^x), and then you get

8 = (3^x)*2*2*(2^x) = 4*((3*2)^x) = 4*(6^x).

Divide both sides by 4:

2 = 6^x.

Then, x = log_6(2). (That's supposed to be read as "the logarithm of 2 with base 6".) You could also take the natural logarithm ("ln") of both sides to get

ln(2) = ln(6^x) = x*ln(6),

which means

x = ln(2) / ln(6)

or, approximately,

x = 0.38685.

Answer 3

x = .6

Answer 4

Start of by replacing 8 with 2^3.

Then, 3^-x = 2^(x-1) Then take the log of both sides...

log(3^-x) = log(2^(x-1))

-x*log(3) = (x-1)*log(2)

-log(3)x = log(2)x - log(2)

-log(3)x - log(2)x = -log(2)

x(-log(3) - log(2)) = -log(2)

x = log(2)/[log(3) + log(2)]

x = log(2)/log(6) = .3868528072

Answer 5

i am not sure what exactly would your teacher tell you as the first step but i would solve for x, then plug x into the equation

Answer 6

I know the answer it is quite simple if you dont know then dodge off school as you must have been dodging school too often in the past
By the way the answer is The Elephant.

Answer 7

theres no real answer cuz it all random stuff, if it is reel, the answer is wat the question is since u put a " = " in it
so i guess the answer is 8/(3^x) or 2^(x+2)

Answer 8

sorry, im too young for this math, good luck though

Answer 9

sorry, im too young for that? that looks really, really hard. good luck

Answer 10

umm............. use a scintific CAQLATER