Question

3) Resolva as seguintes equações exponenciais:
a)3* = 243
b)10^x = 10000
c)2* = 64​

Answer 1

a)3* = 243

3* = 3⁵

* = 5

b)10^x = 10000

10^x = 10⁴

x = 4

c)2* = 64

2* = 2⁶

* = 6

Answer 2

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$\tt a)\\\begin{array}{c|l}\sf243&\sf3\\\sf81&\sf3\\\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\implies\rm 243=3^5\\\sf 3^x=243\\\sf3^x=3^5\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=5}}}}\blue{\checkmark}\\\tt b)~\sf 10^x=10000\\\sf 10^x=10^4\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=4}}}}\blue{\checkmark}\\\tt c)\\\begin{array}{c|l}\sf64&\sf2\\\sf32&\sf2\\\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}\implies\rm 64=2^6\\\sf2^x=64\\\sf 2^x=2^6\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=6}}}}\blue{\checkmark}$