Question Type 4: Constructing, converting and solving Polynomial equations using technology Exercises

Solve the equation $\log_2(x+1)+\log_2(2x+1)=\log_2(6)$ for $x$.

Solve the equation $\log_5(x^2-3x+2)=\log_5(x-1)+1$ for $x$.

Solve the equation $\log_2(2x+1)+\log_2(x-1)=2$ for $x$.

Solve the equation $2\log_{10}(x-1)=\log_{10}(9)$ for $x$.

Solve the equation $2\log_3(x)=\log_9(x^2+2)$ for $x$.

Solve the equation $2\log_3(x-1)=\log_3(x+5)$ for $x$.

Solve the equation $\log_{10}(x-1)+\log_{10}(x-4)=1$ for $x$. [7 marks]

Solve the equation $2\log_3(x+2)=\log_3(2x+5)$ for $x$.

Solve the equation $2\log_2(x)=\log_2(8x-4)$ for $x$.

Solve the equation $\log_3(x)+\log_3(x-2)=2$ for $x$.

Solve the equation $\log_3(x+2)-\log_3(x-1)=2$ for $x$.

Solve the equation $2\log_2(x+1)-\log_2(x-1)=3$ for $x$.