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.

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

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

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