# Discussion of Question with ID = 074 under Logarithms

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### Question

What is P if $\text"log"_5(3)$ + $\text"log"_5(3P + 1)$ = 1 + $\text"log"_5(P + 3)$?

A

3.

B

4.

C

2.

D

2.

Soln.
Ans: a

We have $\text"log"_5(3)$ + $\text"log"_5(3P + 1)$ = $\text"log"_5(5)$ + $\text"log"_5(P + 3)$. It is same as $\text"log"_5(3 × (3P + 1))$ = $\text"log"_5(5 × (P + 3))$. Equating the logs, $3 × (3P + 1) = 5 × (P + 3)$, solving for P we get P = 3.