A scuba diver descends slowly into the ocean at a constant rate. His depth is recorded for the first minutes in the following ta
ble:
a) how much deeper does the diver descend each minute?
b) what is the diver’s depth at minute 7?
c) how long will it take the scuba diver to reach a coral reef that is 120 feet deep?
d) Interpret the meaning of d8 = 96
a) how much deeper does the diver descend each minute?
b) what is the diver’s depth at minute 7?
c) how long will it take the scuba diver to reach a coral reef that is 120 feet deep?
d) Interpret the meaning of d8 = 96
1 answer:
You might be interested in
Answers:
When we evaluate a logarithm, we are finding the exponent, or <u> power </u> x, that the <u> base </u> b, needs to be raised so that it equals the <u> argument </u> m. The power is also known as the exponent.
The value of b must be <u> positive </u> and not equal to <u> 1 </u>
The value of m must be <u> positive </u>
If 0 < m < 1, then x < 0
A <u> logarithmic </u> <u> equation </u> is an equation with a variable that includes one or more logarithms.
===============================================
Explanation:
Logarithms, or log for short, basically undo what exponents do.
When going from to
, we have isolated the exponent.
More generally, we have turn into
When using the change of base formula, notice how
If b = 1, then log(b) = log(1) = 0, meaning we have a division by zero error. So this is why
We need b > 0 as well because the domain of y = log(x) is the set of positive real numbers. So this is why m > 0 also.