Solve the given problems
A medical research lab is growing a virus for a vaccine that grows at a rate of $2.3\%$ per hour. If there are $500.0$ units of the virus originally, the amount present after t hours is given by $N = 500.0(1.023)^{t} .$ How many units of the virus are present after two days?

Plot the indicated semilogarithmic graphs for the following application.
Calculate values of $\phi$ (as negative angles) for the given values of $\omega T$ and plot a semilogarithmic graph of $\phi$ vs. $\omega T$.

solve for y in terms of x. \

$$\frac{\log _7 x}{\log _7 4}-\log _7 y=1$$

Use a calculator to solve the given equations.
$\log (x-3)+\log x=\log 4$

Plot the graphs of the given functions on semilogarithmic paper. \

$$y=3\left(5^x\right)$$

Find the common logarithm of each of the given numbers by using a calculator.
0.0640

Perform the indicated operations if the given changes are made in the indicated examples of this section.
In the previous Example, change the logarithm base to 4 and then plot the graph.

Determine each of the following as being either true or false. \

$$\log \left(\frac{1}{100}\right)=-2$$

Solve the given equations.
$3^x=1 / 81$

Perform the indicated operations on the resulting expressions if the given changes are made in original expressions of the indicated examples of this section.
In the previous Exercise, change the 2 to 3 .

Use a calculator to evaluate (to three significant digits) the given numbers.
$1.5^\pi$

Use logarithms to the base 10 to find the natural logarithms of the given numbers.
6310

Determine the value of the unknown. \

$$\log _b 4=-\frac{1}{3}$$

solve for y in terms of x. \

$$2\left(\log _4 y-3 \log _4 x\right)=3$$