Question

Resolva a equação exponencial abaixo:

0,01^x=10000

Answer 1

$\sf     0.01 {}^{x} = 10000 \\ \\ \\ \sf     \Bigg( \frac{1}{100} \Bigg) {}^{x} = 10000 \\ \\ \\ \sf     \Bigg(\frac{1}{10 {}^{2} } \Bigg) {}^{x} = 10000 \\ \\ \\ \sf     \Big(10 {}^{ - 2} \Big) {}^{x} = 10000\\ \\ \\ \sf     10 {}^{ - 2x} = 10000 \\ \\ \\ \sf     10 {}^{ - 2x} = 10 {}^{4} \\ \\ \\ \sf     - 2x = 4 \\ \\ \\ \sf     x = \frac{4}{ - 2} \\ \\ \\ {\color{red}\boxed{\sf x = - 2}}$

Att: Nerd1990

Answer 2

Resposta:

X = -2

Explicação passo-a-passo:

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$\mathtt{ {0,01}^{x} = 10000 } \\ \mathtt{ {\left( \frac{1}{100} \right)}^{x} = 10000} \\ \mathtt{ {\left( \frac{1}{ {10}^{2} } \right)}^{x} = 10000} \\ \mathtt{\left( {10}^{ - 2} \right) ^{x} = 10000} \\ \mathtt{ {10}^{ - 2x} = 10000} \\ \mathtt{ {10}^{ - 2x} = {10}^{4} } \\ \mathtt{ {\cancel{\blue {10}}}^{ - 2x} = {\cancel{\blue {10}}}^{4} } \\ \mathtt{ - 2x = 4} \\ \mathtt{x = \frac{4}{ - 2} } \\ \red{\mathtt{x = - 2}}$