61. $${\text{If 1}}{{\text{0}}^x}{\text{ = }}\frac{1}{2}{\text{ then 1}}{{\text{0}}^{ - 8x}} = ?$$
62. $$\left( {\frac{1}{{1.4}} + \frac{1}{{4.7}} + \frac{1}{{7.10}} + \frac{1}{{10.13}} + \frac{1}{{13.16}}} \right)$$ is equal to = ?
63. Given that $$\sqrt 5 $$ = 2.236 and $$\sqrt 3 $$ = 1.732, then the value of
$$\frac{1}{{\sqrt 5 + \sqrt 3 }}{\text{ is = ?}}$$
64. If $${\left( {\frac{3}{5}} \right)^3}{\left( {\frac{3}{5}} \right)^{ - 6}} = {\left( {\frac{3}{5}} \right)^{2x - 1}}$$ then x is equal to ?
65. If $${\text{5}}\sqrt 5 \times {5^3} \div {5^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}}$$ then the value of a is = ?
66. if $${{\text{2}}^x} = \root 3 \of {32} $$ then x is equal to = ?
67. $$\sqrt {12 + \sqrt {12 + \sqrt {12 + .....} } } $$ is equal to = ?
68. If $${{\text{5}}^{\left( {x + 3} \right)}}{\text{ = 2}}{{\text{5}}^{(3x - 4)}}$$ then the value of x is = ?
69. $$\frac{{{2^{n + 4}} - 2\left( {{2^n}} \right)}}{{2\left( {{2^{n + 3}}} \right)}}$$ when simplified is = ?
70. If $$a = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}}$$ and $$b{\text{ = }}\frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}}$$ then the value of $$\left( {\frac{{{a^2} + ab + {b^2}}}{{{a^2} - ab + {b^2}}}} \right)$$ is = ?
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