MAH-CET 2026 — Mathematics PYQ

Step 1: Understand the definition of a logarithm

The fundamental mathematical property relating a logarithm to its exponential counterpart states that if:

$${\log }_{b}a=c$$

Then, it can be converted directly into an exponent equation as:

$$a=b^c$$

Where:

• $b$ is the base of the logarithm

• $c$ is the exponent/power

• $a$ is the argument value

Step 2: Apply the definition to the given problem

We are given the logarithmic equation:

$${\log }_{2}X=5$$

By identifying the components from our rule:

• Base ($b$) = $2$

• Power ($c$) = $5$

• Argument ($a$) = $X$

Converting this structural form into an exponential equation yields:

$$X=2^5$$

Step 3: Simplify the exponential value

Calculate the value of $2$ raised to the power of $5$:

$$2^5=2\times 2\times 2\times 2\times 2=32$$

Therefore:

$$X=32$$

Correct Answer

(c) $32$