How do you condense #-5 log_b (y) - 6 log_b (z) + 1/2 log_b (x+4)#?

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Answer 1 · 2016-07-16T18:31:50

=#log_b [sqrt((x+4))/(y^11)]#

All the terms are logs to the same base.

Use the power law first:

#-5 log_b (y) - 6 log_b (z) + 1/2 log_b (x+4)#

=#-log_b (y) ^5- log_b (z)^6 + log_b (x+4)^(1/2)#

If logs are added, the numbers are multiplied. if logs are subtracted, the numbers are divided.

=# log_b [((x+4)^(1/2))/(y^5 xx y^6)]#

=#log_b [sqrt((x+4))/(y^11)]#