903/IMO. problem / Math - Solved Math Problems

MR-903 / 3. problem

Solve the equation over the set of real numbers

$\frac{2 \cdot {(2^{2})}^{3}}{2^{4}} = 2^{x}$

Source: Hungary: 2025 - Unified final exam for high schools - Mathematics - Intermedate level [06.05.2025.] - 3..)

Algebra → Exponential equations and inequalities → Exponential equations

$\frac{2 \cdot {(2^{2})}^{3}}{2^{4}} = 2^{x}$

$\frac{2 \cdot 2^{6}}{2^{4}} = 2^{x}$

$\frac{2^{7}}{2^{4}} = 2^{x}$

$2^{7 - 4} = 2^{x}$

$2^{3} = 2^{x}$

$x = 3$