Not sure how to do logs on the this calculator?

Syntax errors. Check you are inputting your data in the correct order.

The 30XIIS only calculates logs to base e (natural log, ln) and base 10 (common log, log). However logs to any base can be calculated indirectly.
To calculate log base b of x, calculate either log(x)/log(b) or ln(x)/ln(b).

Type solve(log(x^5,16)-log(125,64)+log(x^(1/2),4),x,0.5
Its equation with guess 0,5. Then press enter and you will give result
x=5^(1/3)=1.70997
Or, you can use equation solver with eqn=0(MATH, then B option)
See captured images below

You may want to insist on using the DMS (degree, minute, second) notation but since 20 minutes is 1/3 of a degree the value of the argument of the tangent function is just 36 and 1/3.
Make sure the angle unit is set to degree.
Set the calculator IO mode to MathIO: Press [SHIFT][MODE ][ : Degree]

Press the[ log] button: log(
Press the [ tan] function key tan (
You see on the screen log ( tan (
Type in 36 [a b/c] 1 [a b/c] 3
Close the two parentheses ))
Press [EXE]
You should get -0.13344355615

You can calculate logs to any base by using the relationship
log-base-b(x) = log(x) / log(b) = ln(x) / ln(b)

So, to calculate the log base 2 of 32, for example, calculate log(32) and divide by log(2).

Use the LOG key on the top row for common logs, the LN key for natural logs. In either case, simply enter the number as given then press the appropriate log key, then press =.

Since I do not know what Kenko calculator you have I will remain general.

Locate a key marked log (for common decimal logarithm)
Try the two options. One of them is bound to work

1. Enter a positive number and press the key marked LOG.
2. If that does not work, press the LOG key and then enter a positive number. If the calculator displayed log( , with a left parenthesis, insert a right parenthesis before pressing the = key.

To calculate the natural logarithms (LN), look for a key marked with LN and proceed as for the common logarithm. I am sure that the syntax (key sequence) that works for the common log will work for th natural log.

If no key is marked on top of it with LOG or LN, it may be because those markings are ON the body of calculator. In that case the functions are accessed by pressing a key marked SHIFT or 2ND, or 2ndF before the function LOG or LN.

Use the relation log5(x) = log(x) / log(5) = ln(x) / ln(5)

LOG ( 1 / 625 ) / LOG 5 =

or

LN ( 1 / 625 ) / LN 5 =

It's simple 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
you just need to know that the default base of log in calculators is 10, so log x mean
log x base 10 = log x / log 10,
so write log x / log y for log x base y example:
log 8 base 2 = log 8 / log 2 that is how you write it on calculator, hope it was helpful

It's very simple: the calculators have a default base 10 so that log x it's log x base 10 so here is some logs:
log x base y = log x / log y
log (x*y) = log x + log y
log (x/y) = log x - log y
Hope it's helped