Question

Halp please...
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If loga(2) = logb(16) show that b=a^4

Answer 1

@jim_thompson5910 @Kainui Help please

Answer 2

Hint: use the change of base rule


loga(2) = logb(16)


log(2)/log(a) = log(16)/log(b)

Answer 3

ahh yes i did that then i couldnt think of a way to go futher :P

Answer 4

loga(2) = logb(16)


log(2)/log(a) = log(16)/log(b)


log(2)*log(b) = log(a)*log(16)

Answer 5

then what

Answer 6

im a slow thinking hold on a min :P

Answer 7

can you even times logs together?

Answer 8

Yeah, there's nothing wrong with multiplying logs together.

Answer 9

log2b =log16a??
Im guessing :P

Answer 10

no thats not correct

Answer 11

loga(2) = logb(16)


log(2)/log(a) = log(16)/log(b)


log(2)*log(b) = log(a)*log(16)


log(b)/log(a) = log(16)/log(2)


then what?

Answer 12

log(b)*log(2) = log(a)*log(16)

Answer 13

why would you go back a step?

Answer 14

oh umm my bad

Answer 15

would you multiply everything by log a?

Answer 16

why not convert use the change of base formula and simplify the left side

Answer 17

loga(b)? =log(16)/log(2)

Answer 18

now what is log(16)/log(2)

Answer 19

log2(16)?

Answer 20

use a calculator if you're not sure

notice that log(16)/log(2) is the same as log2(16)

yes

Answer 21

and that is?

Answer 22

4

Answer 23

AHH I GET IT NOW :P
:D

Answer 24

so you would get

loga (b) = 4

Answer 25

ok good