How to express this equation in terms of m and n ?
Given #log_8 3 = m# and #log_8 5 = n# , express #log_3 50# in terms of m and n.
Given
1 Answer
Sep 4, 2017
Explanation:
We need to know the logarithm rules:
#log_a(bc)=log_a(b)+log_a(c)# #log_a(b^c)=clog_a(b)# #log_a(b)=log_c(b)/log_c(a)# #log_a(a)=1#
Then:
#log_3(50)=log_8(50)/log_8(3)=log_8(50)/m#
Splitting up
#=log_8(2*5^2)/m=(log_8(2)+log_8(5^2))/m=(log_8(8^(1/3))+log_8(5^2))/m#
#=(1/3log_8(8)+2log_8(5))/m=(1/3+2n)/m=(1+6n)/(3m)#