F(-6) = (-6)2 + 2(-6)
= -12 - 12
= -24
<h3>Answer: Check out the screenshots below.</h3>
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Explanations:
Part 1
For the first box, we use the log rule that log(A)+log(B) = log(A*B)
Then in the second box, we'll convert to exponential form. The logs are assumed to be base 10.
The third box then factors and uses the zero product property.
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Part 2
We check each solution generated in part 1.
Plugging x = 5/3 will lead to the same number on each side. Therefore, x = 5/3 is a true solution.
In contrast, plugging x = -2 leads to a false equation. Recall that the domain of y = log(x) is x > 0. This means we cannot replace x with negative numbers. The value x = -2 is extraneous.
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Part 3
There's not much to explain here that isn't already done so on the screenshot below.
11/12 as a fraction is 11/12; as a decimal it is ~ 0.9167

and 10.6 is already written as a decimal.
Compounded once a year: A=P(1+r)^t
2500=500(1+0.095)^t
1.095^t=5
because the unknown number is an exponent, use log to find the unknown:
log(1.095^t)=log5
tlog1.095=log5
t=log5/log1.095
use your calculator, t=17.734
so this person is about 28 years old.