NIMCET 2022 — Mathematics PYQ

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Question

NIMCET 2022 — Mathematics PYQ

NIMCET | Mathematics | 2022

The value of $3^{3 - l o g_{3} 5}$ is:

Choose the correct answer:

Explanation

Solution

To find the value of the expression $3^{3 - \log_{3} 5}$ , we use the laws of exponents and logarithms.

Step 1: Use the exponent rule $a^{m-n} = \frac{a^m}{a^n}$

3^{3 - \log_{3} 5} = \frac{3^3}{3^{\log_{3} 5}}

Step 2: Simplify the numerator

3^3 = 27

Step 3: Simplify the denominator using the logarithmic identity $a^{\log_{a} x} = x$

3^{\log_{3} 5} = 5

Step 4: Combine the results

\frac{27}{5}

Final Answer:

The value is $\frac{27}{5}$ . (Option B)