# Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.3 - Page 477: 88

$$\frac{1}{2}(C-4A)$$

#### Work Step by Step

$\log_b2=A$ and $\log_b3=C$ $$X=\log_b\sqrt{\frac{3}{16}}$$ $$X=\log_b\Bigg(\frac{3}{16}\Bigg)^{1/2}$$ Apply the Power Rule here, we can move the exponent $1/2$ away for Quotient Rule usage later. $$X=\frac{1}{2}\log_b\frac{3}{16}$$ Now we can apply Quotient Rule for $\log_b\frac{3}{16}$ $$X=\frac{1}{2}(\log_b3-\log_b16)$$ $$X=\frac{1}{2}(\log_b3-\log_b2^4)$$ Again, use the Power Rule for $\log_b2^4$ $$X=\frac{1}{2}(\log_b3-4\log_b2)$$ Now we substitute A and C into X $$X=\frac{1}{2}(C-4A)$$

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