Logs

THE GRAPH OF Y=AB^X PASSES THROUGH THE POINTS (2,400) AND (5,50)

(A)FIND VALUES OF THE CONSTANTS A AND B

a=1600
b=1/2

(b)Given that ab^x<k for some content k>0 show that x> log(1600/k)/log2 where log means to any valid base

how does someone do part b?I know the log rules

log a+log b=log ab
log a-log b=log a/log b

I tried to do this:

y=log(!600)+1/2log(1/2) but this isn't taking me anywhere any help is much appreciated I looked at the marks scheme but I don't understand it.

Try using log(1/2) =-log(2)

How will this lead me anywhere?

THE GRAPH OF Y=AB^X PASSES THROUGH THE POINTS (2,400) AND (5,50)

(A)FIND VALUES OF THE CONSTANTS A AND B

a=1600
b=1/2

(b)Given that ab^x<k for some content k>0 show that x> log(1600/k)/log2 where log means to any valid base

how does someone do part b?I know the log rules

log a+log b=log ab
log a-log b=log a/log b

I tried to do this:

y=log(!600)+1/2log(1/2) but this isn't taking me anywhere any help is much appreciated I looked at the marks scheme but I don't understand it.

THE GRAPH OF Y=AB^X PASSES THROUGH THE POINTS (2,400) AND (5,50)

(A)FIND VALUES OF THE CONSTANTS A AND B

a=1600
b=1/2

(b)Given that ab^x<k for some content k>0 show that x> log(1600/k)/log2 where log means to any valid base

how does someone do part b?I know the log rules

log a+log b=log ab
log a-log b=log a/log b

I tried to do this:

y=log(!600)+1/2log(1/2) but this isn't taking me anywhere any help is much appreciated I looked at the marks scheme but I don't understand it.

There are a couple of things wrong with your first try, taking logs of
Y=AB^X
gives
log(Y) = log(A) + log(B^X)
and remember the other log property (which is just a bigger log(AB) = log(A)+log(B))
log(B^X) = X*log(B)
Can you take it from there using post 2?
If not, can you show your working up to the point where you're confused.

I did:
log(ab^x) < log(k)
log(a) + log(b^x) < log(k)
log(1600) + xlog(1/2) < log(k)
But am super confused on where to go now?
How can I get it so that X is on the greater side of the <?