The number of pages in the IRS Tax Code has increased from $400$ pages in 1913 to $70,320$ pages in 2009. The increase can be modeled by the exponential function

$$T(x)=400(1.055)^x,$$

where $x$ is the number of years since 1913. Use this function to estimate the number of pages in the tax code for 1950, 1990, and for 2000. Round to the nearest one.

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$

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$

Use a graphing calculator to find the approximate solutions of the equation. $\\$$0.082 e^{0.05 x}=0.034$

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.

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.

$\log _b \frac{3}{b}$

Use a graphing calculator to find the approximate solutions of the equation. $\\$$2^x-5=3 x+1$

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

$$\log _a 3$$

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)=x^3-1$

Find each of the following using a calculator. Round to four decimal places. $\\$$\ln 2$

Express in terms of sums and differences of logarithms.

$$\log \sqrt[3]{\frac{M^2}{N}}$$

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)= $$ \frac{5 x-3}{2 x+1}$ $$

Solve the exercise below: $\\$$2 \log 50=3 \log 25+\log (x-2)$