Evaluating Logarithms. Find the value of the given variable. \( \begin{array}{lll}\text { 1. } \log _{4} 16=x & 3 \cdot \log _{x} 1000=3 & \text { 5. } \log _{3} x=4 \\ \text { 2. } \log _{27} \frac{1}{3}=z & \text { 4. } \log _{m} 81=4 & \text { 6. } \log _{5} y=2\end{array} \)

Gegee die funksie \( f(x)=3^{-x} \). 6.1 Gee die vergelyking van \( g \) indien \( g \) die refleksie van \( f \) in die \( y \)-as is en wat 3 eenhede afwaarts geskuif word. B.2 Bereken die \( x \)-afsnit van \( g \).

Diketahui fungsi tujuan meminimumkan \( Z=x+5 y \) dengan pembatas-pembatas sebagai berikut \( x+y \leq 8 \) \( 2 x-3 y \leq 6 \) \( x \leq 5 \) \( y \geq 1 \) a. gambarkan daerah layak b. tentukan Z minimum

Use propenties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1 . Where possible, evaluate logarithmic expressions. \( 7 \ln (x-4) \) - \( 3 \ln x \)

Determine whether the following statment is true or false. The graph of \( y=\frac{1}{7} g(x) \) is the graph of \( y=g(x) \) stretched by a factor of 7 . Choose the correct answer below. A. True, because the graph of the new function is obtained by adding 7 to each \( x \)-coordinate. Balse, because the graph of the new function is obtained by multiplying each \( y \)-coordinate of \( y=g(x) \) by \( \frac{1}{7}<1 \). C. True, because the graph of the new function is obtained by multiplying each \( y \)-coordinate of \( y=g(x) \) by 7 and \( 7>1 \). D. False, because the graph of the new function is obtained by adding 7 to each \( x \)-coordinate.

A 25 -year old woman burns \( 350-70 t \) cal/hr while walking on her treadmill. Her caloric intake from drinking Gatorade is \( 135 t \) calories during the \( t \) th hour. What is her net decrease in calories after walking for 4 hours?