Write the following logarithms in terms of the natural logarithm. Then use a calculator to find the value of the logarithm, rounding your result to four decimal places.


${\log }_{6}60$

Solving equations Solve each equation.

√2 sin 3Θ + 1 = 2, 0 ≤ Θ ≤ π

Find the inverse $f^{-1}\(\left\)(x\(\right\))$ of each function (on the given interval, if specified).

$f\(\left\)(x\(\right\))=10^{-2x}$

State whether the functions represented by graphs A , B , C and in the figure are even, odd, or neither. <IMAGE>

Evaluate each expression without a calculator.

a. log₁₀ 1000

Find the inverse $f^{-1}\(\left\)(x\(\right\))$ of each function (on the given interval, if specified).

$f\(\left\)(x\(\right\))=\(\frac{2}{x^2+1}\)$, for $x\(\geq{0}\)$

The National Weather Service releases approximately $70,000$ radiosondes every year to collect data from the atmosphere. Attached to a balloon, a radiosonde rises at about $1000$ ft/min until the balloon bursts in the upper atmosphere. Suppose a radiosonde is released from a point $6$ ft above the ground and that $5$ seconds later, it is $83$ ft above the ground. Let $f\(\left\)(t\(\right\))$ represent the height (in feet) that the radiosonde is above the ground $t$ seconds after it is released. Evaluate $\(\frac{f\left(5\right)-f\left(0\right)}{5-0}\)$ and interpret the meaning of this quotient.