Question

ALGUÉM ME AJUDAR POR FAVOR!!!

Calcule o valor dos seguintes logaritmos: ​

Answer 1

a)

$log_{16}(64) = log_{ {2}^{4} }( {2}^{6} ) = \frac{6}{4} = \frac{3}{2}$

b)

$log_{625}( \sqrt{5} ) = log_{ {5}^{4} }( {5}^{ \frac{1}{2} } ) = \frac{ \frac{1}{2} }{4} \\ = \frac{1}{8}$

c)

$log_{49}(\sqrt[3]{7}) = log_{ {7}^{2} }( {7}^{ \frac{1}{3} } ) = \frac{ \frac{1}{3} }{2} = \frac{1}{6}$

d)

$log_{ \sqrt[5]{2} }(128) = log_{ {2}^{ \frac{1}{5} } }( {2}^{7}) = \frac{7 }{ \frac{1}{5} } \\ = 7.5 = 35$

e)

$log_{9}(3 \sqrt{3} ) = log_{ {3}^{2} }( {3}^{ \frac{3}{2} } ) \\ = \frac{ \frac{3}{2} }{2} = \frac{3}{4}$

f)

$log_{2}( \sqrt[8]{64}) = log_{2}( {2}^{ \frac{3}{4} } ) = \frac{ \frac{3}{4} }{2} \\ = \frac{3}{8}$

Answer 2

Explicação passo-a-passo:

a) 2^6 = 2^4x

4x = 6 --> x = 6/4 --> x = 3/2

b) 5^1/2 = 5^4x

4x = 1/2 --> x = 1/8

c) 7^1/3 = 7^2x

1/3 = 2x --> x = 1/6

d)2^7 = 2^1/5x

1/5x = 7 --> x= 35

e)3.3^1/2 = 3^2x

3/2 = 2x --> x = 3/4

f)8^2.1/8 = 2^1x

1/4 = 1x --> x = 1/4

Bons estudos!