Question

Tìm x ∈ Z, biết:

a, \(\dfrac{3}{2}\). 4^x + \(\dfrac{5}{3}\)^. 4^x+2 = \(\dfrac{3}{2}\)^. 4⁸ + \(\dfrac{5}{3}\)^. 4¹⁰

b, (1/3 + 1/6) . 2^x + 2^x+1 = 2¹² + 2¹⁰

c, (1/2 - 1/3 ) . 6^x + 6^x+2 = 6¹⁵ + 6¹⁸

d, \(\dfrac{5}{3}\). 8^x+2 - \(\dfrac{3}{5}\) . 8^x = \(\dfrac{5}{3}\)^. 8¹¹ - \(\dfrac{3}{5}\). 8⁹

Answer 1

a: \(\Leftrightarrow4^x\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)=4^8\left(\dfrac{3}{2}+\dfrac{5}{3}\cdot4^2\right)\)

=>4^x=4^8

=>x=8

b: \(\Leftrightarrow2^x\cdot\dfrac{1}{2}+2^x\cdot2=2^{10}\left(2^2+1\right)\)

=>2^x=2^11

=>x=11

c: =>1/6*6^x+6^x*36=6^15(1+6^3)

=>6^x=6*6^15

=>x=16

d: \(\Leftrightarrow8^x\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)=8^9\left(\dfrac{5}{3}\cdot8^2-\dfrac{3}{5}\right)\)

=>x=9