11.5k views
4 votes
Solve for x. Round to the nearest thousandth.
16^2^x =33

*Show work*

User Dnsko
by
7.7k points

2 Answers

7 votes

Answer:


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

User Mark Pauley
by
7.3k points
0 votes
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.
User Hitokage
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories