Question

Resolva em R as equações exponenciais pfvr me ajudem ..

a) $9^{x} = 1$

b) $32^{x+1} = \sqrt{8}$

c)$( \frac{1}{25} ) ^{3x-2} =625$

d) $125^{x+2} = 25^{x+5}$

e) $8^{x+2}=1$

f) $343^{3x-2} = 49^{2x}$

Answer 1

9ˣ = 1
(3²)ˣ = 1
3²ˣ = 3⁰
2x = 0
x = 0

-------------------

32ˣ⁺¹ = √8
(2⁵)ˣ⁺¹ = (2³)^¹/₂
5(x + 1) = ³/₂
5x + 1 = ³/₂
10x + 2 = 3
10x = 1
x = ¹/₁₀

---------------------

(5⁻²)³ˣ⁻² = 5⁴
-2(3x - 2) = 4
-6x + 4 = 4
-6x = 0
x = 0

-----------------------

3x + 6 = 2x + 10
x = 4

----------------------

3x + 6 = 0
3x = -6
x = -2

----------------------

9x - 6 = 4x
5x = 6
x = ⁶/₅