# Question #e10e6

##### 1 Answer

#### Answer:

#### Explanation:

The only way to get the answer

#m = -100#

is to have

#log(-m) + 2 = 4#

as your starting equation. As you know, the **common log**, which is denoted **log base**

#log_10 (-m) + 2 = 4#

The first thing to do here is isolate the log on one side of the equation by adding

#log_10 (-m) + color(red)(cancel(color(black)(2))) - color(red)(cancel(color(black)(2)))= 4 -2#

#log_10(-m) = 2#

The log function is actually *undefined* for **negative numbers** when working with *real numbers*. This tells you that

Now, the log function is the **inverse operation** to exponentiation. This means that you're looking for a number that is equal to the **base**, which in your case is

#log_color(red)(10)(color(blue)(-m)) = color(darkgreen)(2)#

Can thus be rewritten as

#color(red)(10)^color(darkgreen)(2) = color(blue)(-m)#

Since

#100 = -m implies m = color(green)(|bar(ul(color(white)(a/a)color(black)(-100)color(white)(a/a)|)))#

As predicted,