Math Doubts

Evaluate $2^{2-\log_{2}{5}}$

A special mathematical expression is given in this problem and we have to find the value of this expression.

$2^{\,\displaystyle 2-\log_{2}{5}}$

This mathematical expression is basically an expression in exponential form. The base of the term is $2$ but its exponent is an expression. It represents the subtraction of binary logarithm of five from two.

Express the expression in Rational form

$=\,\,\,$ $\dfrac{2^{\displaystyle 2}}{2^{\displaystyle \log_{2}{5}}}$

Evaluate the expression in the numerator

$=\,\,\,$ $\dfrac{2 \times 2}{2^{\displaystyle \log_{2}{5}}}$

$=\,\,\,$ $\dfrac{4}{2^{\displaystyle \log_{2}{5}}}$

Evaluate the expression in the denominator

$=\,\,\,$ $\dfrac{4}{5}$

Ashok Kumar B.E. - Founder of Math Doubts

Ashok Kumar, B.E.

Founder of Math Doubts

A Specialist in Mathematics, Physics, and Engineering, dedicated to helping students master math concepts from basics to advanced levels with clarity and precision.

Story of Math Doubts