Question

Resolva 3^x=2^x+2^x-1

Answer 1

Resposta: x = 1

Explicação passo-a-passo:

3^{x} = 2^{x} + 2^{x-1}  

3^{x} = 2^{x} + \frac{2^{x}}{2^{1}}

2 . 3^{x} = 2 . 2^{x} + 2^{x}

2 . 3^{x} = 3 . 2^{x}

log2(2 . 3^{x}) = log2(3 . 2^{x})

log2(2) + log2( 3^{x}) = log2(3) + log2(2^{x})

1 + x . log2(3) = log2(3) + x . 1

x . log2(3) - x = log2(3) -1

x . (log2(3) - 1) = log2(3) -1

x = 1

Answer 2

Resposta:

S = { 1 }

Explicação passo-a-passo:

$3^{x}=2^{x}+2^{x-1}\\\\3^{x}=2^{x}+\frac{2^{x}}{2}\\\\2.3^{x}=2.2^{x}+2^{x}\\\\2.3^{x}=3.2^{x}\\\\\frac{2^{x}}{3^{x}}=\frac{2}{3}\\\\(\frac{2}{3})^{x}=(\frac{2}{3})^{1}\\\\x=1$