91Ó°ÊÓ

Express as a single logarithm and, if possible, simplify. $$\log 10,000-\log 100$$

Sketch the graph of the function and check the graph with a graphing calculator. Describe how each graph can be obtained from the graph of a basic exponential function. $$f(x)=2^{x+3}-5$$

Graph the function and determine whether the function is one-to-one using the horizontal-line test. $$f(x)=|x+2|$$

Choose the correct name of the principle or rule from the given choices. $$principle of zero products$$ $$ multiplication principle for equations$$ $$product rule addition$$ $$ principle for inequalities$$ $$power rule multiplication$$ $$principle for inequalities$$ $$principle of square roots$$ $$quotient rule$$. If \(a b=0\) is true, then \(a=0\) or \(b=0,\) and if \(a=0\) or \(b=0,\) then \(a b=0 .[3.2]\).

Convert to a logarithmic equation. \(8^{1 / 3}=2\)

Convert to a logarithmic equation. \(10^{0.3010}=2\)

Solve the logarithmic equation algebraically. Then check using a graphing calculator. $$\log _{125} \frac{1}{25}=x$$

Graph the function and determine whether the function is one-to-one using the horizontal-line test. $$f(x)=-0.8$$

Choose the correct name of the principle or rule from the given choices. $$principle of zero products$$ $$ multiplication principle for equations$$ $$product rule addition$$ $$ principle for inequalities$$ $$power rule multiplication$$ $$principle for inequalities$$ $$principle of square roots$$ $$quotient rule$$. $$\text { If } x^{2}=k, \text { then } x=\sqrt{k} \text { or } x=-\sqrt{k} .[3.2]$$

Express as a single logarithm and, if possible, simplify. $$\ln 54-\ln 6$$