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Grade 11Algebra

solve for x: x-1/log₃(9-3^x)-3>=1

chinmay mishra

12 Years agoGrade 11

1 Answer

SHAIK AASIF AHAMED

12 Years ago

$x-1\geq$ log₃(9-3^x)-3

$x-1\geq$ log₃(9-3^x)-log₃₂₇

$x-1\geq$ log₃((9-3^x)/27)

$x-1\geq$ log₃((3^-1-3^x-3))

3^x-1 $\geq$ 3^-1-3^x-3

3^x $\geq$ 1-3^{x-2 (multiplying with 3 on both sides)}

9.3^x $\geq$ 9-3^{x (multiplying with 9 on both sides)}

10.3^x $\geq$ 9

3^x $\geq$ 0.9

x $\geq$ log₃0.9

so X $\geq$ -0.095

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IIT Delhi

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