Logarithms!!! These are hard?

Question

So who knows how to solve logarithms? can anyone solve this problem for me? it will really help me alot..


Evaluate: loga a3

its log then the first a is small and at the botton like where the period (.) belongs. the next a is in the middle and the 3 at the very top.

Answer 1

log-a a³ =3* log_a a = 3,
because log_a a = 1.

Answer 2

First of all when you want to show a power, you can use the ^ symbol (shift 6). Fore ex, x squared is x^2.I know what your saying.
Logarithms become much easier with practice and realizing that they are like powers but written in a different way.

For ex., if you want to say y=x^2 in logarithmic form, you would say log of y with base x equals 2. In the log notation it would be log_x y=2. Of course, it looks a little different when you're not typing it into a computer and you make the x small and at the bottom like you said.

So one of the first steps is just learning how to read them or say them. I know this may seem complicated, but its not with practice converting powers to logs. It takes practice to get comfortable with.

The answer to your question is "3". The first a that is small at the bottom...that is called the base. So the base is "a". So ask, what power do I have to raise a to to get a^3. You have to raise a to the 3rd power to get a^3.

First become comfortable with powers, then become comfortable with putting it in log form. This was a pain for me b/c, although I was comfortable with powers, I wasn't used to seeing it in log form. I wasn't used to thinking this way and I found it easy to forget and get confused. But keep at it and it will get easier. the truth is it isn't that complicated once you get it, but I think it does take practice. This problem seems complicated if you are not comfortable with expressing powers in log form.
Here are some basic examples:

log_2 8=3 You would say this as: log of 8 with base 2 is equal 3. All this is really saying is 2^3=8 but its confusing if your not used to it. The two is the 'lowered number'. It's the base, so ask 2 to what power gives us 8? The answer is 3 b/c 2^3=8

log_10 100=? 10 to what power is 100? 2 b/c 10^2=100

or how about:

log_4 ?=2 Read this as log of what number with base 4 equals 2? Or in other words 4^2 =? The answer is 16.

I hope this helped.

Answer 3

hiya Steven So, we've log issues, huh....?!? permit's have a looksy. There are various approaches of doing this; i visit objective to do it the least confusing way accessible (least confusing for me, of path). Base 2 logs (log(3)log(12)log(40 8)log(192) + sixteen)¹?² - log(12) + log(40 8) + 10 = (log(3)[2 + log(3)][4 + log(3)][6 + log(3)] + sixteen)¹?² - 2 - log(3) + 4 + log(3) + 10= to this point, we've more desirable each and every thing into words with which we are in a position to apply our calculator different than the term "log(3)." permit's convert that into some thing usable. we are nonetheless in base 2. log(3) = ln(3)/ln(2) Now we are in a position to basically kind the expression into our calculator to sparkling up. It seems that this expression extra effective simplifies into: ([ln(3)/ln(2)][2 + ln(3)/ln(2)][4 + ln(3)/ln(2)][6 + ln(3)/ln(2)] + sixteen)¹?² + 12. This expression may well be entered into your calculator, term by term, to get the decimal approximation to the respond for which you're looking, or, extra simplification is accessible: sixteen + ln(3)ln(192)/ln²(2) In any journey, the respond comes out to 20-eight.021881133, approximately. wish that enables! alice

Answer 4

Assume that log refers to base 3 in this example.
y = log a³
y = 3.log a
y = 3 x 1
y = 3