Logarithmic equations Quiz 1

Question 1

Solve for $$x: \log 4x - \log 8 = \log {12_{}}$$

Accepted Answer

$$24$$

Answer

$$15$$

Answer

$$\;10$$

Answer

$$\;12$$

Question 2

Simplify. $$\dfrac{{{{\log }_5}81}}{{{{\log }_5}16}}$$

Accepted Answer

$${\log _2}3$$

Answer

$${\log _3}2$$

Answer

$${\log _{81}}16$$

Answer

$${\log _{16}}81$$

Question 3

If $$5 = {\log _2}p$$ , then find the value of $$p$$

Accepted Answer

$$32$$

Answer

$$25$$

Answer

$$16$$

Answer

$$64$$

Question 4

Given that $$4\log a = \dfrac{{24}}{{\left( {\dfrac{{\log 25}}{{\log 8}}} ight)\left( {\dfrac{{\log 10}}{{\log 5}}} ight)}}$$ . Find $$a 	ext{( All the log expressions are to the base 10)}$$

Accepted Answer

$${2^9}$$

Answer

$${2^{10}}$$

Answer

$${2^8}$$

Answer

$${2^{12}}$$

Question 5

If $$a = {b^2} = {c^3} = {d^4} = {e^5}$$ , then find $${\log _a}abcde$$

Accepted Answer

$$\dfrac{{137}}{{60}}$$

Answer

$$\dfrac{{135}}{{60}}$$

Answer

$$\dfrac{{49}}{{60}}$$

Answer

$$21$$