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Algebra: Logarithms

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1. The value of e ln 1+ ln 2+ ln 3 is ?
2. If logN(25) - logN(81) = 2, then N is?
3. Solve for x: log5( x) + log5(2x +13) = log5(24)
4. Find the coefficient of the fourth term in the expansion of (2x +3y)^11

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Solution Summary

Logarithm problems are solved. Algebraic functions are analyzed for logarithms.

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1.)
exp(ln(1) +ln(2) + ln(3))
= exp(ln(1*2*3)) (because ln(a) + ln(b) = ln(a*b))
= exp(ln(6))
= 6 (because e^(log_base_e (x)) = x) --Answer

2.)
log_base_N(25) - log_base_N(81) = 2
=> log_base_N(25/81) = 2 (because log(m) - log(n) = log(m/n))
=>N^2 = 25/81 (because ...

Solution provided by:

Amrit Lal Ahuja, PhD (IP)

Education

BEng, Allahabad University, India
MSc , Pune University, India
PhD (IP), Pune University, India

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