Question

For each sentence below, find the value of x that makes each sentence true. (5^1/5) 5 = 25 x = (8^1/3)^ 2 = 4 x =

Answer 1

Given:

`(5^{(1)/(5)})^5=25^x`

Let's find the value of x that satisfies the equation.

Rewrite the equation:

`25^x=(5^{(1)/(5)})^5`

Apply the power rule:

`\begin{gathered} 25^x=5^{(1)/(5)\ast5} \\ \\ 5^(2x)=5^{(1)/(5)\ast5} \end{gathered}`

Since the bases of both sides are the same (5), strike them out:

`2x=(1)/(5)\ast5^{}`

Solve for x:

`\begin{gathered} 2x=(5)/(5) \\ \\ 2x=1 \end{gathered}`

Divide both sides by 2:

`\begin{gathered} (2x)/(2)=(1)/(2) \\ \\ x=(1)/(2) \\ \\ x=0.5 \end{gathered}`

ANSWER:

x = 0.5 or ½