Solving exponential equations Quiz 1

Question 1

Find the value of $$x$$ as per given equation $${\left( {\dfrac{1}{2}} \right)^{3x}} > {\left( {\dfrac{1}{2}} \right)^{2x + 3}}$$

Accepted Answer

$$x < 3$$

Answer

$$x > 3$$

Answer

$$x > 2$$

Answer

$$x < 2$$

Question 2

Calculate the given exponential equation $${3^x} - {3^{x + 1}}$$

Accepted Answer

$$ - {3^x}$$

Answer

$${2^x}$$

Answer

$$ - {2^x}$$

Answer

$${3^x}$$

Question 3

Simplify $$ {\left( {\sqrt p } \right)^{\frac{2}{3}}}\sqrt {{q^4}}  \div \sqrt {p{q^{ - \dfrac{1}{2}}}}$$

Accepted Answer

$$\dfrac{{{q^{\frac{9}{4}}}}}{{{p^{\frac{5}{6}}}}}$$

Answer

$$\dfrac{{{q^{\frac{4}{9}}}}}{{{p^{\frac{5}{3}}}}}$$

Answer

$$\dfrac{{{q^{\frac{8}{4}}}}}{{{p^{\frac{5}{9}}}}}$$

Answer

$$\dfrac{{{q^{\frac{7}{4}}}}}{{{p^{\frac{5}{9}}}}}$$

Question 4

Calculate the  $${\left( {\dfrac{{{x^p}}}{{{x^q}}}} ight)^{{p^2} + pq + {q^2}}} 	imes {\left( {\dfrac{{{x^q}}}{{{x^r}}}} ight)^{{q^2} + qr + {r^2}}} 	imes {\left( {\dfrac{{{x^r}}}{{{x^p}}}} ight)^{{r^2} + rp + {p^2}}} = $$ ?

Accepted Answer

$$1$$

Answer

$$x$$

Answer

$${x^{pqr}}$$

Answer

$${x^{p + q + r}}$$

Question 5

Calculate the $$\dfrac{{{2^n} + {2^{n - 1}}}}{{{2^{n + 1}} - {2^n}}} = $$ ?

Accepted Answer

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

Answer

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

Answer

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

Answer

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