Question

3^x - 3^(x-1) =81
Find the value of x
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Answer 1

$HEYA \: \\ \\ 3 {}^{x} - 3 {}^{(x - 1)} = 3 \\ \\ 3 {}^{x} - 3 {}^{ x} \times 3 {}^{ - 1} = 3 \\ \\ put \: \: 3 {}^{x} = z \\ \\ z -( z \div 3) = 3 \\ \\ 2z = 3 {}^{2} \\ \\ z = 9 \div 2 \\ \\ \\ 3 {}^{x} = 3 {}^{2} \div 2 \\ \\ taking \: log \: on \: both \: sides \: we \: have \\ \\ log(3 {}^{x} ) = log(3 {}^{2} ) - log(2) \\ \\ becoz \: \: log(m \div n) = log(m) - log(n) \\ \\ x log(3) = 2 log(3) - log(2) \\ \\ x = (2 log(3) - log(2) ) \\ \: \: \: \: \: \: \: - - - - - - - - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: log(3)$