Question

Solve for x
9^x=3^x+3

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Answer 1

Answer:

${9}^{x} = {3}^{2x}$

now,

${3}^{2x} - {3}^{x} - 3 = 0$

$let \: {3}^{x} = y$

so eq become

${y}^{2} - y - 3 = 0$

$y = \frac{1 + \sqrt{13} }{2}$

y can't be –ve so taken +ve only

i.e

${3}^{x} = \frac{1 + \sqrt{13} }{2}$

$x = log_{3}( \frac{1 + \sqrt{13} }{2} ) \: ans.$

Answer 2

Answer:

answer in attachment. excuse my handwriting.