Question

1) resolva as seguintes equações exponenciais:

Answer 1

Resposta:

a) x = 6

b) x = 2

c) x = 3

d) x = 3

e) $x= -\frac{3}{2} = -1,5$

Explicação passo a passo:

a) $2^x=64$

64 | 2

32 | 2

16 | 2

8 | 2

4 | 2

2 | 2

1 |

|$2\times2\times2\times2\times2\times2\\2^{2} \times 2^{2} \times 2^{2}\\2^{2+2+2} =2^{6}\\\\2^{x} =2^{6}\\x = 6$

b) $6^{x} = 36$

36 | 6

6 | 6

1 |

$6\times6=6^{2}\\6^{x} =6^{2}\\\\x=2$

c) $10^{x} = 1000$

1000 | 10

100 | 10

10 | 10

1 |

$10\times10\times10=10^{3} \\10^x=10^{3} \\x=3$

d) $x^{3} =27$

$x^{3} =27\\x=\sqrt[3]{27}\\x=3$

e) $9^{x+3} =27$

$9^{x+3} =27\\(3^{2})^{x+3} =3^3\\2 (x+3)=3\\2x+6=3\\2x=3-6\\2x=-3\\x= -\frac{3}{2} = -1,5$