Logarithmic Expressions and Equations Help?

Question

Evaluate the following expressions. Show your work.

log(base 3)27

log(base 2)32

log(base 4)1/64

log(base 3)18

log 100

Solve the following logarithmic equations. Show your work.

log(base x)16 = 4

log(base d)12 = 6

log(base x + 4)125 = 3

logx = 3

log(base 7)(2x^2 - 1) = log(base 7)4x

Answer 1

you MUST learn the definition of logarithms in order to do a large majority of log problems.  

Def:   log(base b) N = E if and only if N = b^N

So I will do a couple of your problems and then you do the rest.

1.  log(base 3) 27 = x.  So 27 = 3^x or 3^3 = 3^x which implies that x = 3.

6.  log(base x)16 = 4 implies that 16 = x^4.  But 16 = 2^4.  Therefore x = 2