2^x*5^(3x)=4^(2x+1)

Find X, im assuming?

\(2^x*5^{3x} = 4^{2x+1}\)

Lets go ahead and take the natural log of each side

\(ln{2^x}*ln{5^{3x}} =ln{ 4^{2x+1}}\)

Then bring down those exponets and pull out the x's on the left

\(x(ln{2}*(3)ln{5}) = (2x+1)*ln{4}\)

Pull the X's over to the right and natural log's to the left

\(\frac{ln{2}*(3)ln{5}}{ln{4}} = \frac{2x+1}{x}\)

Simplify

(ln(2)+3(ln(5)))/ln(4) = 3.98289

(2x+1)/x

You can split these into 2x/x and 1/x

becomes 2+1/x

3.98289 = 2+1/x

1.98289 = 1/x

1.98289x = 1

x = 1/1.98289 = 0.5043

x = .5043

Good work SpawnofAngel    :)