Question

Eu e meu amigo colocamos e ninguém nos ajudou só pegaram os pontos; Socorro!!!
n façam isso.

Exercícios:
1) Qual o valor dos logaritmos abaixo:

A) log₃ 81 = x
B) log₂ 64 = x
C) log₂ 32 = x
D) log₃ 1/81 = x

2) Calcule o valor de x.
a) log₅ x =2
b) log₃ x = 0
c) log₂ x = -3
d) logₓ 9 = 2
e) log √7 (1/49) = x

3) Determine o valor das expressões abaixo aplicando as propriedades do
logaritmos:
log₃ 3

b) log₅ 1

c) 4 log₄ 7

d) log₃ 4x = log₃ 16

Answer 1

Explicação passo-a-passo:

1)

A)

$log_{3}81 = x \\ \\ {3}^{x} = 81 \\ \\ {3}^{x} = {3}^{4} \\ \\ \Large \boxed{ \green{ x \bf \: = 4}}$

B)

$log_{2}64 = x \\ \\ {2}^{x} = 64 \\ \\ {2}^{x} = {2}^{6} \\ \\ \Large \boxed{ \green{ x \bf \: = 6}}$

C)

$log_{2}32 = x \\ \\ {2}^{x} = 32 \\ \\ {2}^{x} = {2}^{5} \\ \\ \Large \boxed{ \green{ x \bf \: = 5}}$

D)

$log_{3} \frac{1}{81} = x \\ \\ {3}^{x} = \frac{1}{81} \\ \\ {3}^{x} = \frac{1}{ {3}^{4} } \\ \\ {3}^{x} = {3}^{ - 4} \\ \\ \Large \boxed{ \green{x \bf = - 4}}$

2)

a)

$log_{5}x = 2 \\ \\ {5}^{2} = x \\ \\ x = 5 \times 5 \\ \\ \Large \boxed{ \green{ x \bf \: = 25}}$

b)

$log_{3}x = 0 \\ \\ {3}^{0} = x \\ \\ \Large \boxed{ \green{x \bf \: = 1}}$

c)

$log_{2}x = - 3 \\ \\ {2}^{ - 3} = x \\ \\ x = {2}^{ - 3} \\ \\ x = \frac{1}{ {2}^{3} } \\ \\ \Large\: \boxed{ \green{x\: \bf = \frac{1}{8}} }$

d)

$log_{x}9 = 2 \\ \\ {x}^{2} =9 \\ \\ x = \sqrt{9} \\ \\ \Large \boxed{ \green{x \bf \: = 3}}$

e)

$log_{ \sqrt{7} }( \frac{1}{49} ) = x \\ \\ { (\sqrt{7}) }^{x} = \frac{1}{49} \\ \\ { ({7}^{ \frac{1}{2} } )}^{x} = \frac{1}{49} \\ \\ {7}^{ \frac{x}{2} } = \frac{1}{ {7}^{2} } \\ \\ {7}^{ \frac{x}{2} } = {7}^{ - 2 } \\ \\ \frac{x}{2} = - 2 \\ \\ x = 2 \times ( - 2) \\ \\ \Large \boxed{ \green{x \bf \: = - 4}}$

3)

a)

$log_{3}3 = x \\ \\ {3}^{x} = 3 \\ \\ {3}^{x} = {3}^{1} \\ \\ \Large \boxed{ \green{x \bf \: = 1}}$

b)

$log_{5}1 = x \\ \\ {5}^{x} = 1 \\ \\ \Large \boxed{ \green{ x \bf \: = 0}}$

c)

$4. log_{4}7 = x \\ \\ log_{ {2}^{2} }( {7}^{4} ) = x \\ \\ x = \frac{4}{2} log_{2}7 \\ \\ \Large \boxed{ \green {x = 2 log_{2}7}}$

d)

$\red{log_{3}}4x = \red{ log_{3}}16 \\ \\ 4x = 16 \\ \\ x = \frac{16 }{4 } \\ \\ \Large \boxed{ \green{ x = \bf 4}} \\ \\ \Large \boxed{ \underline{ \blue{ \bf \: Bons \: Estudos!} \: \bf \: 20/05/2021}}$

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