log5P x logp x = 2. What is the value of x?a)125b)P2c)25d)51/2Correct answer is option 'C'. Can you explain this answer?

Question

Answer

This can be further expand as-logP/log5 × logx/lopP = 2
Now eliminating logP
We get logx/log5=2 log5(X)=2X=5^2=25

Answer

We can write this equation as (log p)/(log5)*(log x)/(log p)=2
=> (log x)/(log5) = 2
=> it can be written as (log x) base 5= 2
so, x = (5)² x=25hence C is correct.

Answer

C.25

Answer

To solve the given equation log5P x logp x = 2 and find the value of x, we can use the properties of logarithms and algebraic manipulation.

Let's break down the steps to solve the equation:

Step 1: Rewrite the equation using the properties of logarithms.
log5P x logp x = 2
log5P + logp x = 2

Step 2: Combine the logarithms using the product rule of logarithms.
log5Pp x = 2

Step 3: Rewrite the equation in exponential form.
5^2 = Pp

Step 4: Simplify the equation.
25 = Pp

Step 5: Since we need to find the value of x, we need to determine the value of P. To do that, we can use the given options.

Option A: 125
If P = 125, then the equation becomes:
25 = 125p
Dividing both sides by 125, we get:
1/5 = p
However, this contradicts the given equation since logp x = 1/5, not 2. Therefore, option A is incorrect.

Option B: P^2
If P = P^2, then the equation becomes:
25 = (P^2)p
This simplifies to:
25 = P^(2+p)
Again, this contradicts the given equation since the left side is a constant (25) while the right side is a variable (P). Therefore, option B is incorrect.

Option C: 25
If P = 25, then the equation becomes:
25 = 25p
Dividing both sides by 25, we get:
1 = p
This satisfies the given equation since logp x = 1, and it also matches the simplified equation. Therefore, option C is correct.

Option D: 5^(1/2)
If P = 5^(1/2), then the equation becomes:
25 = (5^(1/2))p
Taking the square of both sides, we get:
625 = 5^p
This does not match the given equation, so option D is incorrect.

Therefore, the correct answer is option C) 25.

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