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7-29.

Given $\log _{b} M = 2.1$, $\log_{b} N = 0.6$ and $\log _{b} P = −1.8$, find $\log b \frac { \sqrt { N P } } { M ^ { 2 } }$.

Break this up into many logs. Then substitute the given values.

$\log_{b}\sqrt{N}+\log_{b}\sqrt{P}-\log_{b}M^{2}$

$\left ( \frac{1}{2} \right )\text{log}_{b}N+\left ( \frac{1}{2} \right )\text{log}_{b}P-2\text{log}_{b}M$

Substitute the known values in the expression above.