1-2-7 معادلات تجمع أكثر من فكرة

مثال 1: حل 2ˣ⁺³ ÷ 4ˣ = 32.

الحل:

4ˣ = 2²ˣ

2ˣ⁺³⁻²ˣ = 2³⁻ˣ

32 = 2⁵

3 − x = 5

x = −2

مثال 2: حل 3²ˣ⁻¹ = 27ˣ⁻¹.

الحل:

27ˣ⁻¹ = 3³ˣ⁻³

\[\begin{gathered}2x - 1 = 3x - 3\end{gathered}\]

x = 2

مثال 3: حل 5ˣ × 25 = 3125.

الحل:

25 = 5²

5ˣ\[\begin{gathered}^{+2} = 3125 = 5^{5}\end{gathered}\]

x + 2 = 5

x = 3

مثال 4: إذا كان 2ˣ = 5 فأوجد 2ˣ⁺² و 2²ˣ.

الحل:

2ˣ⁺² = 2ˣ × \[\begin{gathered}2^{2} = 5 \times 4 = 20\end{gathered}\]

2²ˣ = (2ˣ)² = 25