exponents

I've got a problem which I am not sure of the method of solving.

3^x + 3⁶ x 2 = 3⁷

3^x + 729 x 2 = 3⁶ x 3

3^x + 1458 = 729 x 3

3^x = 2187 - 1458

3^x = 729

3^x = (3)⁶

x = 6

But isnt there any other method of solving? Please help

4 Answers

Since 3⁷ = 3⁶ x 3 ,

3^x = (3⁶ x 3) - (3⁶ x 2) = 3⁶[3 - 2] = 3⁶

So x = 6

I really understand how you got the RHS ?? Not getting it.

Please explain .

3^x + 3⁶ x 2 = 3⁷

3^x= 3⁷ - 3⁶ x 2

3^x= 3⁶ [3- 2] = 3⁶

x=6

Does this make life simpler?

Thanks a lot! :) Now I understand.

√ √ || {} [] () → ~ ^ x x x → → ln log lg lim lim cos sin tan cot arcsin arccos arctan

∫ ∫ ∫ ∫ ∫ ∬ ∬ ∬ ∬ ∬ ∭ ∭ ∭ ∭ ∭ ⨌ ⨌ ⨌ ⨌ ⨌

∑ ∑ ∑ ∑ ∑ ∮ ∮ ∮ ∮ ∮ ∏ ∏ ∏ ∏ ∏ ∐ ∐ ∐ ∐ ∐

+ - × ÷ ± ∓ = ∪ ∩ ≠ ∼ ≈ ∅ ∀ ∃ ∈ ∋ ∝ ≤ ≥ ≃ ≅ ≡ < > ≪ ≫ ⊂ ∉ ⊃ ⊆ ⊇ ⇒ ⇐ ⇔ ⇒ ⇐ ⇔ ⇑ ⇓ ⇕ → ← ↔ → ← ↔ ↑ ↓ ↕ ↖ ↗ ↘ ↙ ↪ ↩ ⇀ ↼ ⇁ ↽

° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω