log(4)(log(2)16)
WILL MEDAL AND FAN PLEASEEE HELP

Question

anonymous · Answer

$$\log_{4}(\log_{2}16) $$

anonymous · Answer

Also this problem if you can help me on this one too. its my last homework problems that i have no idea how to do

campbell_st · Answer

well 16 = 2^4

so for base 2 logs its log(16) = log(2^4) = 4log(2)   = 4

because the base of the log and base of the exponential are the same, the value is 1.  

so then its base 4 logs for  log(4) 

hopefullt this helps

anonymous · Answer

im even more confused now

knowledge · Answer

lets do this step by step
what is $$\log _{2}16$$

campbell_st · Answer

srtart with the base 2 log

rewrite 16 as 2 to the power 4 and apply the log law for power

$$\log_{2}(16) = \log_{2}(2^4) = 4\log_{2}(2)$$

and when the base of the log and the base of the exponent are the same the answer is 1

$$\log_{a}(a) = 1$$

so 

$$\log_{2}(2) = 1$$



$$4 \times \log_{2}(2) = 4 \times 1 = 4$$

so you now have 

$$\log_{4}(4) = ?$$

apply the same log law... base of the log and base of the exponent are the same...