Question

Solve 5 superscript 3x baseline equals index root 3 start root 25 end root.
(1 point)
Responses

x = 2
x = 2

x equals start fraction 1 over 2 end fraction
Image with alt text: x equals start fraction 1 over 2 end fraction

x equals start fraction 2 over 9 end fraction
Image with alt text: x equals start fraction 2 over 9 end fraction

x = 1

Answer 1

To solve the equation \( 5^{3x} = \sqrt[3]{\sqrt{25}} \), we first simplify the right-hand side.

1. Start with the expression inside the cube root:
\[
\sqrt{25} = 5
\]

2. Now take the cube root:
\[
\sqrt[3]{5}
\]

So we rewrite the equation:
\[
5^{3x} = 5^{1/3}
\]

3. Since both sides have the base \(5\), we can set the exponents equal to one another:
\[
3x = \frac{1}{3}
\]

4. Now, solve for \(x\):
\[
x = \frac{1}{3} \div 3 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]

However, this result is not shown in the response options you've provided. Let's recheck the solution process thoroughly or verify the original equation again.

In conclusion:
- After rechecking, the original equation \( 5^{3x} = \sqrt[3]{\sqrt{25}} \) simplifies correctly to \( 5^{3x} = 5^{1/3} \), leading to \( 3x = \frac{1}{3} \) and thus \( x = \frac{1}{9} \), not listed in your provided options.

Make sure you're sharing the right equations or explore corrections to existing responses if there was an error.