Simplifying Logarithmic Expressions
Find the domain of the logarithmic function and then graph the function
\[
y=\ln (5 x+2)
\]
Find the domain of the function
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.)
Expanding Logarithmic Expressions
Write the following as a sum of logarithms:
\[
\ln \left(\frac{e^{3} x^{4}}{y^{5}}\right)=\square+\square \ln (x)+\square \ln (y)
\]
Exponential Expressions
10. The graph of $y=f(x)=b^{x}$, where $b>1$, is translated such that the equation of the new graph is expressed as $y-2=f(x-1)$. The range of the new function is
Exponential Equations
Suppose that a company introduces a new computer game in a city using television advertisements. Surveys show that $\mathrm{P} \%$ of the target audience buy the game after $x$ ads are broadcast, satisfying the equation below. Complete parts (a) through (d).
\[
P(x)=\frac{100}{1+51 e^{-0.1 x}}
\]
a) What percentage buy the game without seeing a TV ad $(\mathrm{x}=0)$ ?
$\%$
(Type an integer or a decimal rounded to the nearest tenth as needed.)
Evaluating Logarithms
Evaluate the logarithm \(\log_5{125}\)
Rewriting in Exponential Form
Rewrite the logarithmic equation \(\log_{2}(x) = 5\) in exponential form.
Converting to Logarithmic Form
Convert the exponential equation \(2^5 = 32\) to its equivalent logarithmic form.
Converting to Radical Form
Convert the exponential equation \(5^{x} = 125\) to radical form.