Solve Each Equation for the Given Variable

Analysis Page 2

Logarithmic Equations

Solve each equation for the given variable.

1. log7x=127 2. log35x=114 3. log8x-4=97

4. ln5x+2=7 5. ln4x-9=-49 6. ln2xx+3=3

7. logx-45=3 8. lnx+4+lnx+7=ln15x+24

9. log167x-log16x+1=12 10. log45x-log4x-8=3

11. log1004-x+log100x+8=log100(2-3x)

12. log5(4x-7)5=3

13. lnx-6+ln2x+5=2lnx 14. log6x-8+log6x+8=2

15. 2ln5+ln(3x-1)=2ln10 16. logx+21+logx=2

17. log2x+5+logx-4=log⁡(x2+20)

18. log7x+12-log7x-3=2 19. log23x2+16=6

20. log5(2x+3)+log5(x-6)=3 21. log642x+1=23+log64x

22. log6(10x+20)-log6(x2-3)=2 23. log9(2x+3)2=3

Instructions: Solve for x in terms of y.

24. logx-y=log⁡(4x+2) 25. logx-y=log⁡(4x+2)

26. log3x-y-log3(x+y)=1 27. logy2-4x=3+logyx

28. The equation 3log64x2+6x=2 has two solutions. Find the sum of the two solutions.