Hello Colin,

39,44 and 48 are some of those problems in which we can't just use one log and cancel everything nicely in one step, however, we can use any log to bring down the exponents using the power rule. Look for example at:

$$2^{-4x+1} = 3^{2x-3}$$

If we use $\ln$ on both sides, the exponents would come down like

$$\ln\left(2^{-4x+1}\right) =\ln\left( 3^{2x-3}\right)$$

$$\left(-4x+1\right)\ln\left( 2 \right)  = \left(2x-3\right) \ln\left (3 \right),$$

and now we have a nice linear equation with solution

$$x = \frac{\ln\left( 2 \right) + 3\ln\left( 3 \right)}{4\ln\left( 2 \right) + 2\ln \left( 3\right) } \approx .803$$

For 64, the whole $3x^2$ is inside the $\log$. Think of it as $\log\left( 3x^2 \right)$. It is common to omit the parenthesis when they are only plugging in one term inside the $\log$.  (Was that the question you had in there, or was is it something else?)

Let me know if you have any more questions,

David