I don't know how to log ...

Im stuck on these:






Can you explain how I do them? Thanks

y=(3)(10^(2x))
y=(3)(10^2)(10^x)
y=300(10^x)

Does that help?

For the other question 1 is equal to log of 10 to base 10, so you can rewrite the RHS as a log of something to base 10 if you also use the first log rule in this page
http://www.adug.org.au/MathsCorner/LOGS1.GIF
(Can't remember it's name)
Then you can take log to base 10 away from both sides, but before this you need to use a certain rule to "fix" the LHS

I still don't get the first one.

But for the second you can re-arrange to:
2 log10 (x/y) = log10 10 + log10 (10x^2 y)
2 log10 (x/y) = log10 (100 x^2 y)
log10 x^2 - log10 y^2 = log10 (100 x^2 y)
x^2 - y^2 = 100 x^2 y

But I dont think that's correct

I still don't get the first one.

But for the second you can re-arrange to:
2 log10 (x/y) = log10 10 + log10 (10x^2 y)
2 log10 (x/y) = log10 (100 x^2 y)
log10 x^2 - log10 y^2 = log10 (100 x^2 y)
x^2 - y^2 = 100 x^2 y

But I dont think that's correct

Im stuck on these:

You are just solving for x

Think what has happened to x and "undo" the functions

You have
x
multiply by 2
raise 10 to the power of
multiply by 3
= y

so reverse the process
y
divide by 3
take log base 10
divide by 3
= x

Ok I tried this method...
a= 0.5 b= 1/3.
Is that right?

How does y/300 turn into y^-300?? Isn't y^-300 = 1/y^300?