Log 3 base 10 - Texas Instruments TI-84 Plus Calculator

Rephrase the question please. It makes no sense, in particular what are all those TIMES for?
Combine all the logs using the rule log_2(a)+log_2(b)=log_2(a*b)
You get
log_2((x-10)(x-3)/x)=2=log_2(4)
Thus
(x-10)*(x-3)/x=4
Convert it to a quadratic equation (x^2-17x+30=0). the solutions are x=2 and x=15. That should not be too difficult to factor out 5*2=30 -15-2=-17.

Press LOG 3 ENTER.

The LOG key on the keyboard gives you base-10 (common) logs while the LN key gives you base-e (natural) logs. If you want the log to another base you can use the logBASE function found in the catalog.

Absolutely. To take the logarithm base b of x, simply divide the logarithm of x by the logarithm of b. You can use either the common (base-10) or natural (base-e) log, as lojng as you're consistent.
To calculate the log base 3 of 9, for example, calculate either
log 9 / log 3
or
ln 9 / ln 3

Calculate the log (base 10) of the number, then divide the result by the log (base 10) of the base.
For example, to calculate the base-3 log of 9, calculate the log of 9 to get 0.954 . Divide that by the log of 3 (about 0.477) to get 2.0 .
Since 9 is 3 squared, the log base 3 of 9 is 2, as we just calculated.

You can calculate the log to any base B by dividing the base-10 log by the log-base-10 of the base B. You can also calculate it by dividing the natural log by the natural log of B.

For example, to calculate the base-3 log of 10, calculate
log(10) / log(3)
or
ln(10) / ln(3)

Most calculators can't do logs in different bases, but you can solve for the answer this way:

Let's say you need to take the log of 5 in base 3. This can also be written as log5 (base 10)/log3 (base 10).

A more technical solution can be found here: http://oakroadsystems.com/math/loglaws.htm#NewBase

4726 seems to already be on base 10
it's 4*10^3 + 7*10^2 + 2*10^1 + 6*10^0

Look it's simple in the calculator the default base is 10 so when you input log 3 its log 3 base 10 so:
maybe you know in math log x base y = log x / log y . So if you need log 3 base 3 its => log 3 / log 3 (by the way its 1)

It's 2*3=6 but about the base, you can't change it in the calculators the default base it's 10 so log x it's Logbase 10^x here some logs:

log x base y = log x / log y
log (x*y) = log x + log y
log (x/y) = log x - log y
in your example log 9 base 3 = log 9 / log 3 etc.
hope you get it, and it was helpful