Question

plzz answer question no 7 plzz

Answer 1

Please see the attachment

Answer 2

$Question \: = > \: If \: {4}^{x} - {4}^{x - 1} = 24 \\ then, \: find \: the \: value \: of \: x \\ \\ Ans \: = > \: To \: make \: the \: calculation \: easier, \: factorise \: the \: expression \\ \\ (4 - 1) \times 4 {}^{x - 1} = 24 \\ \\ subtract \: the \: numbers \\ \\ 3 \times {4}^{x - 1} = 24 \\ \\ divide \: both \: sides \: with \: 3 \\ \\ {4}^{x - 1} = 8$

$write \: in \: exponential \: form \: with \: base \: 2 \\ \\ {(2}^{2} ) {}^{x - 1} = 8 \\ \\ {2}^{2 x - 2} = 8 \\ \\ 8 = 2 \times 2 \times 2 = {2}^{3} \\ \\ {2}^{2x - 2} = {2}^{3} \\ \\ bases \: are \: same \: so \: set \: the \: exponents \: equal \\ \\ 2x - 2 = 3 \\ \\ 2x = 3 + 2 \\ \\ 2x = 5 \\ \\ x = \frac{5}{2} \\ \\ x = 2.5$