Simplifying logarithmic expressions Quiz 1

Question 1

Find the value for ‘b’, where $${\log _a}b = 1000$$and $${\log _2}a = 100.$$

Accepted Answer

$${2^{100000}}$$

Answer

$${2^{100}}$$

Answer

$${2^{1000}}$$

Answer

$${2^{10000}}$$

Question 2

Find the value of $$a$$ if $${\log _2}[{\log _5}({\log _2}a)] = 1$$.

Accepted Answer

$${2^{25}}$$

Answer

$${2^2}$$

Answer

$${2^{20}}$$

Answer

$${2^{16}}$$

Question 3

Find the value of ‘x’ if $$x = \dfrac{{\log \sqrt 8 }}{{\log 2}}$$.

Accepted Answer

$$\dfrac{3}{2}$$

Answer

$$\dfrac{1}{2}$$

Answer

$$1$$

Answer

$$\dfrac{1}{6}$$

Question 4

Express $${\log _{10}}\left( {\dfrac{1}{{50}}} \right)$$ in terms of $$x$$ given $${\log _{10}}5 = x$$.

Accepted Answer

$$ - (1 + x)$$

Answer

$${(1 + x)^{ - 1}}$$

Answer

$$\dfrac{x}{5}$$

Answer

$$\dfrac{1}{{2x}}$$

Question 5

Simplify the term $$\dfrac{{\log \sqrt {27}  + \log 9 + \log \sqrt {81} }}{{\log 27}}$$.

Accepted Answer

$$\dfrac{{11}}{6}$$

Answer

$$1$$

Answer

$$\dfrac{1}{2}$$

Answer

$$\dfrac{3}{5}$$