SOLUTION: Agh...I am having major trouble understanding Logs! Please help?? 1. log x =3 (answers: a.30, b.300, c.1000, d.3000) 2. 9^x=11 (answers: a. 1.0192, b. 1.0913 , c. 1.131

Question 115400: Agh...I am having major trouble understanding Logs!
Please help??
1. log x =3 (answers: a.30, b.300, c.1000, d.3000)
2. 9^x=11 (answers: a. 1.0192, b. 1.0913 , c. 1.1314 , d. 1.1163)
thanks for any help!
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The first of these problems uses the following definition that relates the logarithmic form
to the exponential form:
.
The logarithmic form is equivalent to the exponential form
.
Let's use this relationship on the problem. You are given:
.

.
Compare this to the logarithmic form above. If you do you will see that "a" in the logarithmic
form is 10 in your problem. Also you will see that y in the logarithmic form is 3 in your
problem. And B in the logarithmic form is x in your problem. Now all you have to do to convert
your problem is to go to the exponential form and plug in the corresponding values.
Start with the exponential form and substitute 10 for "a", 3 for y, and x for B.
When you do those substitutions you get as the exponential form of the given problem:
.

.
Cubing 10 results in 1000 and the exponential form reduces to just:
.

.
That is the answer to the first problem ... x = 1000. This is answer c in your list of
answers.
.
The second problem first involves taking the logarithm of both sides to get:
.

.
On the left side you can use the logarithmic property that the log of a quantity that is raised
to an exponent is equal to the logarithm of the quantity multiplied by the exponent.
This means that . Substitute this into the equation and
you then have:
.

.
Now you can use a calculator to find that:
.
and

.
Substitute these values into the equation and you have:
.

.
Solve for x by dividing both sides by 0.954242509 to get:
.

.
After you do the division on the right side ... using a calculator ... you have:
.

.
Answer b in your list of answers is the correct choice.
.
Hope this helps you to understand logarithms a little bit more.
.
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