I have a few - a lot, actually - of doubts with logarithms and some other stuff. Anyone up? I'd be thankful even if you could answer one of these.
Q2. Find the sum of all the solutions of the equation
Q3. Let , , and , be positive integers such that and . If , find the value of .
Q4. If then find the characteristic of to the base 7.
Q5. Find satisfying the equation
Q6. Find the real solutions to the system of equations
Q7. Solve :
Q8. Prove that
Q9. Find the value of
Q10. Find the value of for which the equation has exactly three distinct real roots.
Q11. Find the number of terms of the longest geometric progression that can be obtained from the set . (I think the question does not consider , because the answer given for this one is .)
Q12. If and , where , then prove that has at least two real roots. (I think it should be , but this is what the sheet says.)
Q13. If and are real numbers such that find the minimum value of .
Q14. If the product then find the value of . (where denotes greatest integer less than or equal to .)