Question

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

Answer 1

Use two main properties of powers:

1. $\left(\dfrac{1}{a}\right)^n=a^{-n};$

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

Consider the equation

$\left(\dfrac{1}{3}\right)^{d-5}=81.$

Note that:

1. $\left(\dfrac{1}{3}\right)^{d-5}=3^{-1\cdot (d-5)}=3^{-d+5};$

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

Answer 2

Your answer should be C.