Simplify the exercise below: $\\$$\log _p p^3$

Use a graphing calculator to find the approximate solutions of the equation. $\\$$4 \ln (x+3.4)=2.5$

The central processing unit (CPU) power in computers has increased significantly over the years. The CPU power in Macintosh computers has grown exponentially from 8 MHz in 1984 to 3400 MHz in 2013. The exponential function

$$M(t)=7.91477(1.26698)^t,$$

where $t$ is the number of years after 1984 , can be used to estimate the CPU power in a Macintosh computer in a given year. Find the CPU power of a Macintosh Performa 5320 CD in 1995 and of an iMac G6 in 2009. Round to the nearest one MHz.

The number ot students frón India cmulled in U.S. colleges and universities has grown exponentially from about $9000$ in 1980 to about $95,000$ in 2008. The exponential function

$$I(t) \equiv 9000(1.0878)^t,$$

where $t$ is the number of years since 1980, can be used to estimate the number of students from India enrolled in U.S. colleges and universities. Find the number of students from India enrolled in 1985, in 1999, and in 2006. Then use the function to predict the number of students from India enrolled in 2012.

The number of students from India enrolled in U.S. colleges and universities has grown exponentially from about 9000 in 1980 to about 95,000 in 2008. The exponential function

$$I(t)=9000(1.0878)^t,$$

where $t$ is the number of years since 1980, which can be used to estimate the number of students from India enrolled in U.S. colleges and universities. Find the number of students from India enrolled in 1985, 1999, 2006, and in 2012.

For each function: $\\$ a) Determine whether it is one-to-one.$ $$ b) If the function is one-to-one, find a formula for the inverse. $$ f(x)= $$ \sqrt{x+1}$ $$

Given that $\log _b 2 \approx 0.693, \log _b 3 \approx 1.099$, and $\log _b 5 \approx 1.609$, find each of the following, if possible. Round the answer to the nearest thousandth. $\\$$\log _b 15 b$

Use a graphing calculator to find the approximate solutions of the equation. $\\$$5 e^{5 x}+10=3 x+40$

Given that $\log _a 2=0.301, \log _a 5=0.699$, and $\log _a 6=0.778$, find each of the following. $\\$$\log _a 50$

For each function: $\\$ a) Determine whether it is one-to-one.$

$$b) If the function is one-to-one, find a formula for the inverse.$$

f(x)=4 x^2+3, x \geq 0$

Fiancé(e) Visas. The number of foreign nationals who came to the United States to marry an American using a "fiancé(e) visa" has grown exponentially in recent years. The total number of fiancé(e) visas issued is given by the function

$$f(x)=5728.98(1.1214)^x,$$

where $x$ is the number of years since 1990 (Source: U.S. Department of Homeland Security). Find the total number of fiancé(e) visas issued in 2006 and in 2009.

The central processing unit (CPU) power in computers has increased significantly over the years. The CPU power in Macintosh computers has grown exponentially from $8 \mathrm{MHz}$ in 1984 to $3400 \mathrm{MHz}$ in 2013 (Source: Apple). The exponential function

$$M(t)=7.91477(1.26698)^t,$$

where $t$ is the number of years after 1984, can be used to estimate the CPU power in a Macintosh computer in a given year. Find the CPU power of a Macintosh Performa $5320$ $\mathrm{CD}$ in 1995 and of an iMac G6 in 2009. Round to the nearest one $\mathrm{MHz}$.

Find each of the following using a calculator. Round to four decimal places. $\\$$\ln (-4)$

The number of U.S. troops diagnosed as overweight has more than doubled since 1998. The exponential function

$$W(x)=23,672.16(1.112)^x,$$

where $x$ is the number of years since 1998, which can be used to estimate the number of overweight active troops. Find the number of overweight troops in 2000, 2008, and in 2013.