True or False (Logarithm)

Question

Determine if True or False. 

 

*small # under log

 

1) log*5(xy)=(log*5x)(log*5y)

 

2) log*5 4= log4/log5

                

Answer 1

Those * numbers are not called "small" numbers, and they are not "under" the log.  These numbers are called the "base" so they are placed near the baseline to remind you what they are.

 

The change of base rule works for any base, not just 10, so log_bX = log_m (X) / log_m (b),  for any new base m.  Of course, 10 as well as the natural base e are preferred because they are available on the calculator.

 

The easy way to remember these rules is remind yourself of the exponent rules:

x^a · x^b = x^a+b  (from product of bases, the exponents get added)

log_x (AB) = log_x (A) + log_x (B) etc.

Answer 2

1) log₅(xy)=(log₅x)(log₅y)   False

According to Laws of logarithm,

log₅(xy)= log₅x + log₅y

2) log₅4= log4/log5       True

log_bx = log₁₀x/log₁₀b

Answer 3

1)

log₅ xy = log₅ x + log₅ y        False.

2)

log₅ 4 = log 4 / log 5             Change of Base, True