Question

Solve the exponential equation below, fill in the blank if necessary

Answer 1

Given:

`((1)/(5))^x=6`

Required:

We need to find the value of x.

Step-by-step explanation:

Taking log on both sides.

`log((1)/(5))^x=log6`
`Use\text{ }log(a^x)=xlog(a).`

`xlog((1)/(5))=log6`
`Divide\text{ both sides of the equation by l}og((1)/(5))`

`x(log((1)/(5)))/(log((1)/(5)))=(log6)/(log((1)/(5)))`

`x=(log6)/(log((1)/(5)))`

`Use\text{ }log((a)/(b))=log(a)-log(b).`

`x=(log6)/(log(1)-log(5))`

`Use\text{ }log(1)=0.`

`x=(log6)/(-log(5))`
`x=-1.11328`

`x=-1.113`

Final answer:

`x=-1.113`