Question: Which equation is equivalent to
Option A:
Option B:
Option C:
Option D:
Answer:
Option C:
Solution:
Given expression:
Convert 16 to the base 2 and 32 to the base 2.
Using exponential rule:
Using the rule,
8p = 5p + 15
3p = 15
p = 5
Substitute p = 5 in given expression, we get
<u>To find the equivalent expression to the given expression:</u>
Option A:
Using the rule,
⇒ 4p = 4p + 3
⇒ 0p = 3
No solution for p, so it is not equivalent to the given expression.
Option B:
Using the rule,
⇒ 4p = 4p + 12
⇒ 0p = 12
No solution for p, so it is not equivalent to the given expression.
Option C:
Using the rule,
⇒ 8p = 5p + 15
⇒ 3p = 15
⇒ p = 5
Substitute p = 5 in , we get
It is equivalent to the given expression.
Option D:
Using the rule,
⇒ 8p = 5p + 3
⇒ 3p = 3
⇒ p = 1
Substitute p = 1 in , we get
It is not equivalent to the given expression.
Hence Option C is the correct answer.