pre calculus

the logarithm, Properties of Simple Logarithms log 1=0 log a =1 log a* = x and all.* = x (inverse property) If log. x = log. y then x = y Properties of Natural Logarithms In 1 = 0 In e =1 In e* = x and ex = x (inverse property) If Inx= Iny then x = y A standard logarithm can have any positive number as its base except 1, whereas a natural log is always base e. Since the natural log is always base e, it will be necessary to use a calculator to evaluate natural logs unless one of the first three examples of the properties of natural logs is used. For anything such as In 2 =, a calculator must be used. When dealing with logarithms, switching between exponential and Logarithmic form is often necessary. Logarithmic form Exponential Form log b = c a = b Write each of the following in exponential form. A) log, 16 =2 B) log, 3=- C) log, 27 = N / W E) 1084 16 -=-2 Write each of the following in logarithmic form. A) 34 =81 B) 161/4 =2 C ) 36- 1/2 =- 6 D) 165/4 =32 Simplifying Logarithms Evaluate each of the following logarithms without the use of a calculator. A) log, 81= B) 1084 2 C) log12 144 = 1 = D) 1086 36 E) 1082 4 F) 10go.25 4 = G) 10g, -3= H) log: 4= I) 10g81 27 J) log , 32 = K) log, 0 = L) 10g10 1 = M) log4 8 N) 10827 3 0) log, 3 = P) log6 6 = 1 = Q) 10836 6 R) 10g128 2 = S) log, 16 = T) log, 27* = U) In el? = V) 3 10815 = W) In1 = X) eln4x = Y) log, 16V2 = Z) log, $9 = a) log, 98/3 = b) 1085 3/25 36 c) 1085 25 d) elnsx'=