I am stuck on this one part of this question:

The function S(d)=93(logd)+65 relates the speed of the wind S, in miles per hours, near the centre of a tornado to the distance that the tornado travels,d,in miles. If a tornado has sustained winds of about 250 mph, estimate the distance it can travel.
I do this :
250= 93logd +65
185/93= logd
logd= 0.989247312
I don't know what to do after that because I cannot divide anything by log. Or is there some other way I should be doing this?

You have to take the inverse of log, that is ...

what number d you you need, so that log d = .989...
BTW, I got log d = 1.9892....
hope yours was just a typo.


On most calculators, use the 2ndF key

on mine, I would press the following:

2ndF
log
1.98924..
=

to get 97.5545

Without having to re-enter the 1.98...

Here is the sequence of my keystrokes

250
-
65
=
÷
93
=
2ndF
log
=

to get the 97.5545

To solve for the distance d, you need to isolate it from the equation using logarithmic properties. To remove the logarithm, you need to use the exponential function.

The equation 185/93 = logd can be rewritten as:
logd = 185/93

To eliminate the logarithm, you can rewrite the equation using exponential form:
d = 10^(185/93)

Now you can use a calculator to evaluate the right-hand side of the equation to get the approximate value for d.

d ≈ 10^(185/93) = 65.4607476

So, the approximate distance that the tornado can travel is 65.46 miles.

To solve for the distance the tornado can travel, you need to rewrite the equation in exponential form and isolate the variable.

Step 1: Rewrite the equation in exponential form.
Since the equation is in the form logd = 0.989247312, you can rewrite it as:
d = 10^(0.989247312).

Step 2: Evaluate the expression.
Using a calculator, evaluate 10^(0.989247312). The result is approximately 8.909.

Therefore, the estimated distance the tornado can travel is about 8.909 miles.