need help on logs?

Question

Express log4 3 and log16 3 as logarithms to the base 2. Hence find n if log2n = 2log4 3 + 8log16 3 show all working out.

Answer 1

log (base 4) 3 = log (base 2) 3 / log (base 2) 4
log (base 16) 3 = log (base 2) 3 / log (base 2) 16

log(2) n = 2 log(2) 3 / log(2) 4 + 16 log(2) 3 / log(2) 16
log(2) n = 2 log(2) 3 / 2 log(2) 2 + 16 log(2) 3 / 4 log(2) 2
log(2) n = log(2) 3 + 4 log(2) 3
log(2) n = 5 log(2) 3
2^log(2) n = 2^(log(2) (3^5))
n = (3^5) = 243

Answer 2

I guess you in the first expression mean
4 3=4^3=(2x2)^3=(2^2)^3=2^6
Then the logarithm with basic number 2 is 6

log(2)16^3= 12 because 16^3=¨(2^4)^3=2^12

log2n=2log4^3
2n=(4^3)^2
2n=(((2^2))^3)^2=2^12
n=(2^12)/2=2^11

Answer 3

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