Question

1) Solve for x
2^(5x+4)+2^9=2^10​

Answer 1

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${2}^{5x + 4} + {2}^{9} = {2}^{10}$

${2}^{5x + 4} = {2}^{10} - {2}^{9}$

${2}^{5x} \times {2}^{4} = {2}^{9}$

${2}^{5x} = \frac{ {2}^{9} }{ {2}^{4} }$

${2}^{5x} = {2}^{9 - 4}$

${2}^{5x} = {2}^{5}$

$5x = 5$

$x = 1$

Answer 2

Step-by-step explanation:

taking 2⁹ common from both sides we have,

2⁹(2^(5x+4-9) + 1) = 2⁹×2

cancelling 2⁹

2^(5x-5) + 1 = 2

2^(5x-5) = 2-1 = 1

as we know

if a^b = 1 given a≠1 then b=0

therefore

5x-5 = 0

5x = 5

x = 5/5 = 1