Question

Solve for x. Round to the nearest thousandth.
`16^2^x =33`

*Show work*

Answer 1

`x = 0.631 / x =0.625`

Explanation:

`16^(2x) = 33\\log(16^(2x) )= log(33)\\2x(log(16))=log(33)\\2x=(log(33))/(log(16)) \\2x=1.26109853\\x= 0.631`

`16^(2x) =33\\16^(2x) = 32 + 1\\(2^(4))^(2x) = 2^(5) + 2^(0) \\8x= 5+0\\8x=5\\x=(5)/(8) \\x=0.625`

Answer 2

To solve for x in the equation 16^(2x) = 33, you can take the natural logarithm of both sides:

ln(16^(2x)) = ln(33)

Using the rule that ln(a^b) = b*ln(a), this simplifies to:

2x * ln(16) = ln(33)

Dividing by ln(16), we get:

2x = ln(33) / ln(16)

x = (ln(33) / ln(16)) / 2

Using a calculator, we can approximate x to the nearest thousandth:

x ≈ 0.481

Therefore, the solution to the equation 16^(2x) = 33 rounded to the nearest thousandth is x = 0.481.