Precalculus: Logarithms and Properties of Logarithms

What is the solution of the equation?

Round your answer, if necessary, to the nearest thousandth.

$$100\cdot2^{4x}=15$$

(a)  

Match the following:

Solve for x.

Rewrite the following in the form $$\log\left(c\right)$$ :

$$\log\left(5\right)+\log\left(6\right)$$

(a)  

Rewrite the following in the form $$\log\left(c\right)$$ :

$$\log\left(a\right)+\log\left(b\right)+\log\left(c\right)$$

(a)  

Match the following:

Rewrite the following in the form $$\log\left(c\right)$$

The $$\ln\ e=$$ ​ (a)  

The $$\log10^x$$ =​ (b)  

The $$\ln e^{abc}$$ =​ (c)   ​

The $$\log_bb^{YODA}$$ =​ (d)  

After the closing of the mill, the town of Bakerville experienced a decline in its population. The relationship between the elapsed, $$t$$ , in years, since the closing of the mill, and the population, $$P\left(t\right)$$ , is modeled by the following function.

$$P\left(t\right)=12000\cdot2^{-\frac{t}{15}}$$

In how many years will Bakerville's population be $$5000$$ ?

Round your answer to the nearest hundreth.

(a)  

In Table 1, when x=​ (a)   , y=8.

In Table 2, when x=12, y=​ (b)  

Rewrite the following the logarithm as $$\log\left(c\right)$$ .

$$2\log\left(5\right)$$

(a)  

Which of the following is the solution of the equation?

$$-100\cdot2^{0.5y}=-5$$