Question

I need to simply simplify: log100^4x
Can you help

Answer 1

Would it be 8x?

Answer 2

what base is the log?

Answer 3

I'm assuming 100...all I'm given is log100^4x

Answer 4

I would assume 10.

so the question would be
\[ log_{10}(100^{4x} )\]

Answer 5

there is this log property:
log(a^b)= b*log(a)
I would use that first.

Answer 6

so 4x?

Answer 7

Do it in steps. Can you use log(a^b)= b*log(a) (match to your problem)
to rewrite log(100^(4x))

Answer 8

log100=2

Answer 9

then 2^4x

Answer 10

If the base is 10, that is true. In this case, it is a safe bet they mean log base 10

Answer 11

But back to the question:
Can you use log(a^b)= b*log(a) (match to your problem)
to rewrite log(100^(4x))

If you understand how to do this, you will be able to solve all these type problems.

To use the rule
log(a^b) =b*log(a)

match a and b to your problem.

Answer 12

btw then 2^4x is not the correct answer.

Answer 13

log(100^(4x)) would = 4xlog100.....correct?

Answer 14

Yes. Definitely on the right track. now we can simplify
\[ log_{10}(100) =\]

Answer 15

2

Answer 16

so put it all together: 4*x*2=

Answer 17

8x

Answer 18

That's how you do this type problem. Hope it makes sense.

Answer 19

So I'm correct with 8x?

Answer 20

yes
log(100^(4x)) = 4x log(100)= 4x*2 = 8x

Answer 21

sweet!! Thank you!! I appreciate your time!