Question

Solve the valid solutions of the following equations providing your values for some of them. Write your answers in solution set form. Identify the extraneous solution, if there is.

logb3 + logb(4x - 5) = 2

(provide a value for b which must be an integer greater than 1)

Answer 1

$$\log_b3+\log_b(4x-5)=2$$

$\begin{matrix} b>0 \\ b\not=1\\4x-5>0 \end{matrix}$

$$\log_b(3(4x-5))=2$$

$$3(4x-5)=b^2$$

$$4x-5=\dfrac{b^2}{3}$$

$$x=\dfrac{b^2+15}{12}, b>0, b\not=1$$

$$\big\{\dfrac{b^2+15}{12}\big\},b>0, b\not=1$$

There is no the extraneous solution.