Question

find the value of b if:​

Answer 1

Answer:

${ (\frac{2}{5} )}^{9 - b} \times {(\frac{5}{2} )}^{2 + 3b} = { (\frac{2}{5} ) }^{3b - 6} \\ { (\frac{2}{5}) }^{9 - b} \times { (\frac{2}{5} )}^{ - 1(2 + 3b)} = {( \frac{2}{5} )}^{3b - 6} \\ {(\frac{2}{5}) }^{9 - b - 2 - 3b} = {(\frac{2}{5}) }^{3b - 6}$

SINCE BASES ARE NOW EQUAL WE CAN EQUATE THE POWERS

$9 - b - 2 - 3b = 3b - 6 \\ 7 - 4b = 3b - 6 \\ 7 + 6 = 3b + 4b \\ 7b = 13 \\ b = \frac{13}{7}$