| Topic | Problem | Solution |
|---|---|---|
| None | Write the following expression in expanded form. … | Apply the properties of logarithms to the given expression: \(\log _{9} \frac{(x-1)^{2}}{(x+1)^{5}}… |
| None | Write the following expression in expanded form. … | Write the following expression in expanded form: \(\ln [x(x-1)]\) |
| None | Write the logarithmic equation $\log _{6} x=5$ in… | The logarithmic equation \(\log _{6} x=5\) can be converted to exponential form by using the defini… |
| None | 1. "At baseline the sample had a mean weight of $… | Given that the mean weight of the sample at baseline in kilograms is 113.1 kg. |
| None | Begin with the graph of $f(x)=\log _{2} x$ and us… | The function \(y=\log _{2}(x-2)\) is a transformation of the function \(f(x)=\log _{2} x\). Specifi… |
| None | Graph the function $f(x)=\log _{1 / 3}(x+1)$ by u… | First, we need to understand the basic graph of the function \(y = \log_a x\). When \(a > 1\), the … |
| None | Find the domain of the following function. \[ f(x… | The function given is \(f(x)=\log _{5}(x-6)\). |
| None | Find the logarithm \[ \log _{125} 5 \] \[ \log _{… | The logarithm of a number is the exponent to which another fixed value, the base, must be raised to… |
| None | ? QUESTION Write the expression as a single logar… | First, we recall the properties of logarithms. Specifically, we use the property \(a \log_b(c) = \l… |
| None | Write the expression as a single logarithm. \[ \l… | The given expression is \(\log _{4}(x+9)+\log _{4} x\). |
| None | The population (in thousands) of people of a city… | The population (in thousands) of people of a city is approximated by the function \(P(t)=1100(2)^{0… |
| None | Express in terms of sums and differences of logar… | The given expression is a logarithm of a square root of a product. We can simplify this using the p… |
| None | Suppose a metal block is cooling so that its temp… | To find the temperature after 3.5 hours, we need to substitute \(t=3.5\) into the given equation \(… |
| None | The population (in thousands) of people of a city… | Given the function for population is \(P(t)=1100(2)^{0.1031 t}\), where \(t\) is the number of year… |
| None | A species of fish was added to a lake. The popula… | The initial population size can be found by substituting \(t=0\) into the function \(P(t)\). |
| None | Convert to an exponential equation. \[ \log _{3} … | Convert the given logarithmic equation \(\log _{3} 9=2\) to an exponential equation. |
| None | Write the equation in its equivalent logarithmic … | The given equation is in exponential form: \(6^{4}=1296\). |
| None | The function $f$ is defined piecewise as follows.… | First, we need to find the limit of the function $f(x)$ as $x$ approaches $-2$ from the left. This … |
| None | A species of animal is discovered on an island. S… | A species of animal is discovered on an island. Suppose that the population size $P(t)$ of the spec… |
| None | Fill in the missing values to make the equations … | Given the equations: (a) \(\log _{3} 2-\log _{3} 7=\log _{3} \square\), (b) \(\log _{2} \square+\lo… |
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