inequations

Can someone pls explain this .If possible with examples

If a^f(x)>b
(1)then if b>0
1)we have f(x)>log_ab if a>1
2)f(x)<log_ab if 0<a<1
(2)for a=1 , b<1

1 Answers

1) for a number say k > 1, raising to any power will increase its value.

eg. (2)² = 4

but for any number say 0<k'<1 , raising to power will decrease its value.

Eg. (.2)² = .04

This is the concept in the above thing.

2.) You're taking a = 1. So whatever Real power does a have, it's value will always remain 1.

Eg. 1¹⁰⁰⁰⁰ = 1

And since by condition a^f(x)>b => 1>b.

√ √ || {} [] () → ~ ^ 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