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Magazine Problem 22
Evaluate the given work for correctness. Is the final answer correct? If not, describe the error(s) in the solution. $$ \begin{aligned} 12 \div 6 \times 4-(3-4)^{2} &=12 \div 6 \times 4-(-1)^{2} \\ &=12 \div 6 \times 4+1 \\ &=12 \div 24+1 \\ &=\frac{1}{2}+1 \\ &=\frac{3}{2} \end{aligned} $$
Problem 22
In exercises \(21-24,\) determine the difference quotient of the given function. $$ y(x)=2 x^{2}-5 $$
Problem 22
Solve the given problem for \(X\). $$ 6^{x+\pi}=2 $$
Problem 23
Solve the given problem for \(X\). $$ -15=-8 \ln (3 x)+7 $$
Problem 23
Evaluate the given work for correctness. Is the final answer correct? If not, describe the error(s) in the solution. $$ \begin{aligned} -3^{2}+6 \div 2+(-4)^{2} &=-9+6 \div 2+(-4)^{2} \\ &=-9+6 \div 2+16 \\ &=-9+3+16 \\ &=10 \end{aligned} $$
Problem 23
In exercises \(21-24,\) determine the difference quotient of the given function. $$ f(x)=x^{3}+x^{2}-x $$
Problem 24
Solve the given problem for \(X\). $$ 2^{x}=3^{x-1} $$
Problem 24
Evaluate the given work for correctness. Is the final answer correct? If not, describe the error(s) in the solution. $$ \begin{aligned} \frac{2+(3-5)}{2-2(6+3)}+\sqrt{64+36} &=\frac{2+(-2)}{2-2(6+3)}+\sqrt{64+36} \\\ &=\frac{2-2}{2-2(9)}+\sqrt{64+36} \\ &=\frac{2-2}{2-2(9)}+8+6 \\ &=\frac{2-2}{2-18}+8+6 \\ &=\frac{0}{-16}+14 \\ &=14 \end{aligned} $$
Problem 25
In exercises \(25-27,\) find all real roots of the given function. $$ g(x)=4 x^{2}+2 x $$
Problem 25
Solve the given problem for \(X\). $$ 8=4 \ln (2 x+5) $$
