Find the value of x if

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answer is B.

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Detailed Solution

We know what exponents are.
10×10×10×10 can be written as

Similarly we can we write

An exponent is nothing but a number with power. Even 2 can be written in exponent form just the power will be 1. Hence

.
Now let us consider any exponent equation say

Then we say that

where a is called the base of log, b is called the argument and n is called the exponent of log.
Now in logarithm the base of log and the argument is always positive and the base is never equal to 1.
For example consider

This can be written in logarithmic form as

Let us consider the given equation

Now if we have

then we say that

Hence we get that

is equal to 2, since

.
Now let us substitute

in the equation. Hence we get,

Now again we have

. Then

Hence

can be written as

.
Now taking the square root on both sides we get

.
Hence x = 25 or x = -25
But since x is the base of logarithm hence it cannot be negative. Hence the only value of x is 25.
Hence, option 2 is correct.

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