Question

How do i solve number 2? i am still confused

Answer 1

The expression is given as,

`((1)/(2))^x=8`

Consider the property of indices,

`(1)/(m)=(m)^(-1)`

Then the given expression becomes,

`\begin{gathered} (2^(-1))^x=8 \\ (2^(-1))^x=2^3 \end{gathered}`

Consider the property,

`(m^a)^b=m^((a\cdot b))`

Applying the property to the given expression,

`\begin{gathered} 2^((-1\cdot x))=2^3 \\ 2^((-x))=2^3 \end{gathered}`

Since the base is same, the numbers will be equal only is the exponents are equal,

`\begin{gathered} -x=3 \\ x=-3 \end{gathered}`

Thus, the solution to the given equation is,

`x=-3`