Розв`язки

4^x - 0,25^x-2 = 15 3^x+3^3-x = 12

4^x- (4^-1) ^x-2 = 15 3^x = 12

4^x - 4^2-x = 15 3^2x + 27 - 12 3^x = 0

4^x - = 15 3^x= t, t 0

1. 4 ^2x-16 - 15 4^x =0 2. t² – 12t +27=0

4^x=y; y 0 t₁=3; t₂=9

у² – 15y – 16 =0 3^x = 3 или 3^х = 3²

у₁ = 16, у₂ = 1 х=1, х=2

4^х=16

4^х=4²

Х=2

9^х – 6 3^х – 27 = 0 2^2х -14 2^х – 32=0

3^2х - 6 3^x - 27=0 2^x=t,t 0

3^x = t, t 0 t² -14t – 32 = 0

3. t² – 6t – 27 = 0 4. t₁ = 16; t₂ = -2

t₁ = -3; t₂=9 2^x=2⁴

3^x=3² x=4

x=2

3^2x-2 3^x – 63 = 0 2^2x – 3 2^x – 40 = 0

3x=t, t 0 2^x = t, t 0

5. t² - 2t - 63 = 0 6. t² - 3t – 40 = 0

t₁ = -7; t₂ = 9 t₁ = 8; t₂ = -5

3^x = 3² 2^x = 2³

х = 2 x = 3

3^2x-8 3^x-9=0 10^2x - 11 10^x + 10 = 0

3^x = t ,t 0 10^x=t; t 0

7. t² - 8t – 9 = 0 8. t² - 11t + 10 = 0

t₁ = 9; t₂ = -1 t₁ = 8; t₂=1

3^x=3² 10^x = 10, 10^x = 1

x = 2 x=1, x = 0

VІ тип

1. 77^2x +4(7 3)^x – 3^2x 3=0 2. 2 81^x+1 – 36^x+1 – 3 16^x+1=0

3. 9 16^x - 7 12^x - 16 9^x = 0 4. 3 2^2x + 6^x - 2 3^2x = 0

5. 5 3^2x + 2 15^x – 3 5^2x=0 6. 9 4^x + 5 6^x - 4 9^x = 0

7. ma 8. 2 25^x – 3 10 - 5 4^x = 0

VІ тип