Question

Which equation can be used to find the solution of (13^)d−5 =81 ?

A. −d−5=4

B. d−5=4

C. −d+5=4

D. d + 5 = 4

Answer 1

your answer should be C.

Answer 2

Use two main properties of powers:

1.
`\left((1)/(a)\right)^n=a^(-n);`

2.
`a^n=a^m\Rightarrow n=m.`

Consider the equation

`\left((1)/(3)\right)^(d-5)=81.`

Note that:

1.
`\left((1)/(3)\right)^(d-5)=3^(-1\cdot (d-5))=3^(-d+5);`

2.
`81=3^4.`

Then, the equation will take look

`3^(-d+5)=3^4.`

The bases of the left and right sides are the same, then the powers are the same too.

`-d+5=4.`

Answer: correct choice is C