Dear Students,

1. log(M✖N)=logM+logN

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

3. logM^N = NlogM

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

1. log

2. log

**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

_{x}a = loga/logx2. log

_{a}a = 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: log

_{8}(5) = b. Express log_{4}(10) in terms of b.
Q4. Simplify without
calculator: log

_{6}(216) + [ log(42) - log(6) ] / log(49)
Q5. Simplify without calculator: ((3

^{-1}- 9^{-1}) / 6)^{1/3}
Q6. Express (log

_{x}a)(log_{a}b) as a single logarithm.
Q7. Find a so that the graph of y = log

_{a}x passes through the point (e , 2).
Q8. Find constant A such that log

_{3}x = A log_{5}x for all x > 0.
Q9. Solve for x the equation log [ log (2 + log

_{2}(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?
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