Solve 5 superscript 3x baseline equals index root 3 start root 25 end root.

Question

(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.

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