15. \( \frac{7}{11}=\frac{18}{x+1} \)

Which of the following is equivalent to \( 3 \ln a-\frac{1}{2}\left(\ln b+\ln c^{2}\right) ? \) (1 point) \( \frac{\ln \left(\frac{3 a}{0.5 b^{2} c}\right)}{\frac{3}{2} \ln \left(\frac{a}{b c^{2}}\right)} \) \( \ln \left(\frac{a^{3}}{b c^{2}}\right) \) \( \ln \left(\frac{a^{3}}{c \sqrt{b}}\right) \)

The electricity rates charged by Monroe Utilities in the summer months are as follows. - Base Charge is \( \$ 8.50 \) - First 600 kWh or less at \( \$ 0.05 / \mathrm{kWh} \) - Over 600 kWh at \( \$ 0.08 / \mathrm{kWh} \) The base is a fixed monthly charge, independent of the kWh (kilowatt-hours) used during the month. a. Find an expression for the cost function \( C(x) \) for usage of or under 600 kWh . \( C(x)=\square<x \leq 600 \) b. Find the charge for using 800 kWh . \( \$ \square \)

Select the equation that can be used to solve \( \log _{4}(x+4)+\log _{4}(x-2)=2 \). (1 point) \( x^{2}+2 x-8=0 \) \( x^{2}+2 x-24=0 \) \( x^{2}-2 x-24=0 \) \( x^{2}-2 x-10=0 \)

Rewrite the following as a single logarithmic expression: \( 3 \log _{b} m-2 \log _{b} n \) (1 point) \( \log _{b}\left(\frac{3 m}{2 n}\right) \) \( \log _{b}\left(m^{3} n^{2}\right) \) \( \log _{b}\left(\frac{m^{3}}{n^{2}}\right) \) \( \log _{b}\left(m^{3}-m^{2}\right) \)

Задание 2. Решить неравенства а) \( |3 x-3|>1 \) б) \( |x+3|<x-2 \) в) \( |3 x+2| \leq|5 x-4| \)