log (38)2 = log2/log38 = 1/log38log (38)19 = log19/log38
Combine them:
log2/log38 + log19/log38 = (log2 + log19)/log38
log(6) 9 = log9/log6log(36) 16 = log16/log36
log9/log6 + log16/log36 = (log9 + log16)/(log6 + log36)
log(5) 512 = log512/log5
Since 512 = 2^9 and 8 = 2^3, we have:
log2^9/log5 = 9log2/log5 = log(5) 8
log (38)2 = log2/log38 = 1/log38
log (38)19 = log19/log38
Combine them:
log2/log38 + log19/log38 = (log2 + log19)/log38
log(6) 9 + log(36) 16log(6) 9 = log9/log6
log(36) 16 = log16/log36
Combine them:
log9/log6 + log16/log36 = (log9 + log16)/(log6 + log36)
log(5) 512log(5) 512 = log512/log5
log(5) 8Since 512 = 2^9 and 8 = 2^3, we have:
log2^9/log5 = 9log2/log5 = log(5) 8