Solving Logarithmic Equations Quiz 1

Question 1

Find the value of $$x$$ by solving the following equation: $$ \ {{\log }_{3}}\left( 7x+18 ight)=2$$

Accepted Answer

$$-\dfrac{9}{7}$$

Answer

$$\dfrac{9}{3}$$

Answer

$$\dfrac{9}{7}$$

Answer

$$-\dfrac{9}{3}$$

Question 2

The possible value of $$x$$ which will satisfy the given equation is: $$ \ {{\log }_{5}}\left( 13x-26 ight)={{\log }_{5}}\left( 3x-6 ight)$$

Accepted Answer

$$2$$

Answer

$$1$$

Answer

$$3$$

Answer

$$4$$

Question 3

Find the value of $$x$$ for which the given equation is true. $$ \ {{\log }_{2}}\left( x+1 ight)-{{\log }_{2}}\left( 2x+8 ight)={{\log }_{2}}6$$

Accepted Answer

$$-\dfrac{47}{11}$$

Answer

$$-\dfrac{46}{10}$$

Answer

$$-\dfrac{45}{9}$$

Answer

$$-\dfrac{44}{8}$$

Question 4

If $${{\log }_{12}}\left( {{x}^{2}}-6 \right)={{\log }_{12}}\left( 3x-6 \right)$$, then $$x$$ is

Accepted Answer

$$0,3$$

Answer

$$1,2$$

Answer

$$2,3$$

Answer

$$3,4$$

Question 5

What are the values of $$x$$ which satisfies $${{\log }_{4}}\left( x \right)+{{\log }_{4}}\left( 2x+5 \right)={{\log }_{4}}\left( 3 \right)$$

Accepted Answer

$$-3,\dfrac{1}{2}$$

Answer

$$-1,\dfrac{1}{2}$$

Answer

$$3,-\dfrac{1}{2}$$

Answer

$$1,-\dfrac{1}{2}$$