Question

$3 \times {4}^{x + 1 } - 13 \times {2}^{x} = 140$
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Answer 1

Answer:

x=2

Step-by-step explanation:

$3 \times {4}^{x + 1} - 13 \times {2}^{x} = 140 \\ 3 \times { {2}^{2} }^{x + 1} - 13 \times {2}^{x} = {2}^{2} (35) \\ {2}^{x} (3 \times {2}^{x + 2} - 13) = {2}^{2} (35 + 13 - 13) \\ {2}^{x} (3 \times {2}^{x + 2} - 13) = {2}^{2} (48 - 13) \\ {2}^{x} (3 \times {2}^{x + 2} - 13) = {2}^{2} (3 \times 16 - 13) \\ {2}^{x} (3 \times {2}^{x + 2} - 13) = {2}^{2} (3 \times {2}^{4} - 13) \\ on \: comparing \: we \: get \\ x = 2 \\ x + 2 = 4 \\ i.e \: \: x = 2$