Priklady.euMathematicsLogarithmic EquationsQuadratic Logarithmic Equations

Quadratic Logarithmic Equations

1. Solve:

log(x + 24) + log(x -24) = 2 x > 24

Solution:
log(x + 24) + log(x -24) = 2
log( (x +24)(x – 24)) = log100
(x +24)(x -24) = 100
x² – 576 = 100
x² – 676 = 0
(x – 26)(x + 26) = 0 => x₁ = 26 v x₂ = -26

K = {26}

2. Solve:

logkvadrat1zad

Solution:

logkvadrat1

3. Solve:

logkvadrat3zad

Solution:

logkvadrat3

4. Solve:

logkvadr4zad

Solution:

logkvadr4

5. Solve:

logkvadr5zad

Solution:

Substitution:
logkvadr5

6. Solve:

logkvadr6zad

Solution:

logkvadr6

7. Solve:

logkvadr7zad

Solution:

logkvadr7

8. Solve:

logkvadr8zad

Solution:

logkvadr8

9. Solve:

logkvadr9zad

Solution:

logkvadr9

10. Solve in real numbers:

Solution:

11. Solve in real numbers:

Solution:

12. Solve in real numbers:

Solution:

13. Solve in real numbers:

Solution:

logaritmicke-kvadraticke-rovnice-13-2

14. Solve in real numbers:

logaritmicke-kvadraticke-rovnice-14-1

Solution:

logaritmicke-kvadraticke-rovnice-14-2

15. Solve in real numbers:

logaritmicke-kvadraticke-rovnice-15-1

Solution:

logaritmicke-kvadraticke-rovnice-15-2

16. Solve in real numbers:

Solution:

logaritmicke-kvadraticke-rovnice-16-2

17. Solve in real numbers:

logaritmicke-kvadraticke-rovnice-17-1

Solution:

logaritmicke-kvadraticke-rovnice-17-2

18.Solve in real numbers:

logaritmicke-kvadraticke-rovnice-18-1

Solution:

logaritmicke-kvadraticke-rovnice-18-2

19. Solve in real numbers:

logaritmicke-kvadraticke-rovnice-19-1

Solution:

logaritmicke-kvadraticke-rovnice-19-2

20. Solve in real numbers:

Solution: