Exponents and Log Help!!

I have four problems I need help on:
5a^2/3*4a^3/2
(I believe it's multiplying, the copier messed up)
4a^5/3^3/2

log5(3x+1)=2
(It's log Base 5, as in the 5 there should be below the rest of the equation)

Log5x(x-1)=2
(This is base 10)

Do you have to simplify the exercice(s) with the exponents?

For the logarithmic equations, use:
For example the second one:

(and offcourse if you want to do the solution check: )

what you wants solution or simplification

I have to simplify and evaluate.

Then you've to know the basic rules like for example , ... .
Can you continue with the hint I gave about the logarithmic equations?

Try to do some work by yourself, that's the best way to learn something.

I did the first one very fast, but for the second one, how does the 5x affect the rule? Because I guess it would be 100 = 5x(x-1)

If the equation is:
then indeed .

What about the exercice with the exponents?

I solved the second one by creating a quadratic and bringing everything to one side before factoring. I came up with 5(x-5)(x+4)
Now, I have to figure out the exponents.

Right! and are indeed the solutions (don't forget to check them!)

But your first exercice is not clear, because you're not using brackets.
I guess you've to simplify:

(to simplify, look at the 'basic rule' I gave in one of my previous posts)

For the question: 4a^5/3^3^2, is there some way I can combine both exponents into one fraction?

Thanks for the rules, I will have to remember them! So, again, for the first one:
If I combine the two fractions:
I came up with
20a^10/6

After this, would the answer come out to 10a^10/3

If the exercice is:


Now the second one, can you be more clear with using brackets?

How does it come out to 13/6?

And, the question is:

Because:

For the second one you can use this 'basic rule':

So, I got


And, for the top part, you cross-multiplied both ways and added them both?