SOLUTION: log (base3) x = 1/2 log (base3) 25 - 5 log (base3) 2

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Question 735036: log (base3) x = 1/2 log (base3) 25 - 5 log (base3) 2
Answer by Susan-math(40) About Me  (Show Source):
You can put this solution on YOUR website!
For simplicity of typing I am leaving the base off the logs.
Use the log rules:
first: rloga=log%28a%5Er%29
so %281%2F2%29log+25=log%2825%5E%281%2F2%29%29=log%28sqrt%2825%29%29=log5
and 5log2=log%282%5E5%29=log32
Now use the rule: loga-logb=log%28a%2Fb%29

log5-log32=log%285%2F32%29
so
so logx=log%285%2F32%29
and x=5%2F32