Shortcuts to Solve Logarithms Problems for Competitive Examinations

Dear Students, there are three fundamental formulas in logarithms which we use generally to solve the problems of algebraic expressions. Also we must know few log values. If nothing is written in the base then its understood that here 10 is placed.These formulas are given below.

Important Formulas of Logarithms:

1. log(M✖N)=logM+logN

2. log(M/N)=logM-logN

3. logM^N = NlogM

Few Important log Values to Remember:

log1=0

log0 = undefined

log2=0.301

log3=0.477

log4=0.602

log5=0.698

log6=0.778

log7=0.845

log8=0.903

log9=0.954

log10=1

Few More Formulas of Logarithms:

1. log_xa = loga/logx

2. log_aa = loga/loga

Solve these Questions By Applying Above Formulas:

Q1. Solve the equation (1/2)^(2x + 1) = 1

Q2. Solve x y^m = y x^3 for m.

Q3. Given: log₈(5) = b. Express log₄(10) in terms of b.

Q4. Simplify without calculator: log₆(216) + [ log(42) - log(6) ] / log(49)

Q5. Simplify without calculator: ((3^-1 - 9^-1) / 6)^1/3

Q6. Express (log_xa)(log_ab) as a single logarithm.

Q7. Find a so that the graph of y = log_ax passes through the point (e , 2).

Q8. Find constant A such that log₃ x = A log₅x  for all x > 0.

Q9. Solve for x the equation log [ log (2 + log₂(x + 1)) ] = 0

Q10. Solve for x the equation 2 x b^{4 log}_b^x = 486

Q11. Solve for x the equation ln (x - 1) + ln (2x - 1) = 2 ln (x + 1)

Q12. Find the x intercept of the graph of y = 2 log( sqrt(x - 1) - 2)

Q13. Solve for x the equation 9^x - 3^x - 8 = 0

Q14. Solve for x the equation 4^{x - 2} = 3^{x + 4}

Q15. If log_x(1 / 8) = -3 / 4, than what is x?