Question

Iflog, b=c, is it possible for c to equal a negativenumber? Explain your answer.

Answer 1

`\log _a(b)=c`

Using the definition of the base of a log:

`\log _a(b)=c\equiv a^c=b`

According to this, c could be a negative number, here's why:

Let's try to find the following logarithm:

`\log _2((1)/(8))=c`

Using the definition of the base of a log:

`2^c=(1)/(8)`

We can express 8 as 2³:

`2^c=(1)/(2^3)`

Using the following property:

`a^(-x)=(1)/(a^x)`

We can express the equation as:

`2^c=2^(-3)`

From this, we can conclude that c = -3, therefore it is possible for x to equal a negative number.