how do I write solution for logarithmic problem 16=(1/4)^-2

Question

how do I write solution for logarithmic problem 16=(1/4)^-2

Answer 1

Your problem is: 16=(1/4)^-2

 

There are two ways you can think about this problem one is to take the log of both sides and solve, the other is to follow the form that converts exponential form to logarithmic form. I'll show both ways.

 

first method:

                                        16=(1/4)^-2

take Log/ln of both sides

                              Log 16 = Log ((1/4)^-2)

apply logarithmic property to right hand side (Log a^b = b*Log a)

                              Log 16 = -2Log(1/4)

then apply Log (a/b) = log a - log b

                              Log 16 = -2(Log 1 - Log 4)

solve both sides

                              1.204 = 1.204

 

The problem here is probably asking for the exponential (y = b^x) to logarithmic form (log_b y = x)

exponential form:       so in logarithmic form

y = 16                                     Log_(1/4)16 = -2

b = 1/4

x = -2

 

So your answer should be: Log_(1/4)16 = -2.

 

The point is to exercise your knowledge of changing between the two form. Later you will have to exercise knowing the properties as in the first method.