Question #e10e6

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Question #e10e6

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Answer 1 · 2016-07-10T12:41:54

$m = - 100$ $m=-100$

Explanation:

The only way to get the answer

$m = - 100$ $m = -100$

is to have

$log (- m) + 2 = 4$ $log(-m) + 2 = 4$

as your starting equation. As you know, the common log, which is denoted $log$ $log$ , is actually the log base $10$ $10$ . This means that your starting equation can be rewritten as

${log}_{10} (- m) + 2 = 4$ $log_10 (-m) + 2 = 4$

The first thing to do here is isolate the log on one side of the equation by adding $- 2$ $-2$ to both sides

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

$log_10(-m) = 2$

The log function is actually undefined for negative numbers when working with real numbers. This tells you that $-m >= 0$ , which implies that $m <= 0$ .

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 $color(red)(10)$ , raised to the power of the result, which is $color(blue)(2)$ .

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

Can thus be rewritten as

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

Since $10^2 = 100$ , you will have

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

As predicted, $m<=0$ .

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