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. logxa = loga/logx
2. logaa = loga/loga
Solve these Questions By Applying Above Formulas:
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. logxa = loga/logx
2. logaa = 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 (logxa)(logab) as a single
logarithm.
Q7. Find a so that the graph of y = logax 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 b4 logbx
= 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 9x - 3x
- 8 = 0
Q14. Solve for x the equation 4x - 2 = 3x +
4
Q15. If logx(1 / 8) = -3 / 4, than what is x?
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