Question

Evaluate and simply the problem 7^x=1/49

Answer 1

`x=-2`

Explanation:

we will use the following properties:

`a^b=a^c\implies b=c\\(1)/(a^n)=a^(-n)`

the right hand side is
`(1)/(49)` and since
`49=7^2`, we have it as
`(1)/(7^2)`. using the second property, this is equal to
`7^(-2)`.

then, we have
`7^x=7^(-2)`.

using the first property, we have
`x=-2.`

Answer 2

To solve the equation 7^x=1/49, we can use the property that if a^b=a^c, then b=c. This means that we can rewrite 1/49 as 7^-2, since 7^-2=1/7^2=1/49. Then we have:

7^x=7^-2

x=-2

Therefore, the solution is x=-2. You can check this by plugging it back into the original equation and see that it is true.