b. 3/2 x 16/4 = 1010, 6 =

The given equation is $\frac{3}{2} \times \frac{16}{4} = 10^c$.
First, simplify the multiplication on the left side:

$$\frac{3}{2} \times \frac{16}{4} = \frac{3 \times 16}{2 \times 4}$$ $$\frac{3 \times 16}{2 \times 4} = \frac{48}{8}$$ $$\frac{48}{8} = 6$$

Now the equation becomes:

$$6 = 10^c$$

To find the value of $c$, take the common logarithm (base 10) of both sides of the equation:

$$\log_{10}(6) = \log_{10}(10^c)$$

Using the logarithm property $\log_b(b^x) = x$:

$$\log_{10}(6) = c$$

We can calculate $\log_{10}(6)$ using the values from the previous problem, where $\log 2 = 0.3010$ and $\log 3 = 0.4771$:

$$\log_{10}(6) = \log_{10}(2 \times 3)$$ $$\log_{10}(6) = \log_{10}(2) + \log_{10}(3)$$ $$\log_{10}(6) = 0.3010 + 0.4771$$ $$\log_{10}(6) = 0.7781$$

Therefore, $c = 0.7781$.