# 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

https://brainmass.com/math/basic-algebra/algebra-logarithms-solve-solve-base-9432

#### Solution Preview

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 Summary

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

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