math helo?

3 = 20 (1/2)^2x
log(3) = log[20 (1/2)^2x]
log(3) = log[20 (2)^(-2x)]
log(3) = log[20 (2^2)^(-x)]
log(3) = log[20 (4)^(-x)]

log(3) = log(20) - x log(4)
x log(4) = log(20) - log(3)
x = [log(20) - log(3)] / log(4)


The answer can be rewritten as :
x = [1 + log(2) - log(3)] / [2 log(2)]

Presuming that is:

3 = 20(1/2)^(2x)

Let's start with dividing both sides by 20 to get the factor with the variable by itself:

3/20 = (1/2)^(2x)

Now get the log of both sides:

ln(3/20) = ln[(1/2)^(2x)]

Now we can move the exponent out of the log:

ln(3/20) = 2x ln(1/2)

And divide both sides by 2 ln(1/2)

x = ln(3/20) / (2 ln(1/2))

That is your exact value. A decimal approximation using a calculator is:

x ≈ 1.36848

As a sanity test, if we plug that into the original equation and simplify, we should get close to 3 (But won't be exact due to rounding, but should be good to 5 SF):

3 = 20(1/2)^(2x)
3 ≈ 20(1/2)^(2*1.36848)
3 ≈ 20(1/2)^(2.73696)
3 ≈ 20(0.150000582)
3 ≈ 3.0000116

Close enough to consider our answer to be correct