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Logarithmic Exponential Equations

1. Solve:

log₃(2^x - 7) = 2 2^x > 7

Solution:
log₃(2^x - 7) = 2
log₃(2^x - 7) = log₃3²
2^x – 7 = 3²
2^x – 7 = 9
2^x = 16
2^x = 2⁴
x = 4

K = {4}

2. Solve:

log₂( 9- 2^x) = 3 – x 2^x < 9

Solution:

logexporov

3. Solve:

log₃( 1 + log₃(2^x-7)) = 1 2^x > 7

Solution:
log₃( 1 + log₃(2^x-7)) = 1
log₃( 1+ log₃(2^x-7)) = log₃3
1 + log₃(2^x-7) = 3
log₃(2^x-7) = 2
log₃(2^x-7) = log₃9
2^x-7 = 9
2^x = 16
2^x = 24
x = 4

K = {4}

4. Solve:

log₃(3^x- 8) = 2 – x 3^x > 8

Solution:

logexporov2

5. Solve:

logexporov3zad

Solution:

logexporov3

5. Solve:

logexporov3zad

Solution:

logexporov3

6.Solve:

Solution:

7. Solve:

Solution:

8. Solve:

Solution:

9. Solve:

Solution:

10.Solve:

Solution:

11.Solve in real numbers:

logaritmicke-exponencialne-rovnice-11-1

Solution:

logaritmicke-exponencialne-rovnice-11-2

12.Solve in real numbers:

logaritmicke-exponencialne-rovnice-12-1

Solution:

logaritmicke-exponencialne-rovnice-12-2

13.Solve in real numbers:

logaritmicke-exponencialne-rovnice-13-1

Solution:

logaritmicke-exponencialne-rovnice-13-2

14.Solve in real numbers:

logaritmicke-exponencialne-rovnice-14-1

Solution:

logaritmicke-exponencialne-rovnice-14-2

15.Solve in real numbers:

logaritmicke-exponencialne-rovnice-15-1

Solution:

logaritmicke-exponencialne-rovnice-15-2

16.Solve in real numbers:

logaritmicke-exponencialne-rovnice-16-1

Solution:
logaritmicke-exponencialne-rovnice-16-2

17.Solve in real numbers:

logaritmicke-exponencialne-rovnice-17-1

Solution:

logaritmicke-exponencialne-rovnice-17-2

18.Solve in real numbers:

logaritmicke-exponencialne-rovnice-18-1

Solution:

logaritmicke-exponencialne-rovnice-18-2

19.Solve in real numbers:

logaritmicke-exponencialne-rovnice-19-1

Solution:

logaritmicke-exponencialne-rovnice-19-2

20.Solve in real numbers:

logaritmicke-exponencialne-rovnice-20-1

Solution:

logaritmicke-exponencialne-rovnice-20-2