Question

Calcule o valor de cada expressão :

a) 3 log 16 base 3
B) 2 ^3 + log 5 base 2
C) 6^1 - log 2 base 5
D) 3 ^-2+ log 18 base 3
E) 5 ^log base 3 1/3
F) 4 ^-1/2 ^+2x ^log 5 base 2

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\Large\boxed{\mathsf{3^{log_3\:16} = 16}}$

$\Large\boxed{\begin{array}{I}\tt \mathsf{2^{3 + log_2\:5}}\\\\\mathsf{2^{log_2\:2^3 + log_2\:5}}\\\\\mathsf{2^{log_2\:8 + log_2\:5}\\\\\mathsf{2^{log_2\:(8.5)}}\\\\\mathsf{2^{log_2\:40} = 40} \end{array}}}$

$\Large\boxed{\begin{array}{I}\tt \mathsf{6^{1 - log_6\:2}}\\\\\mathsf{6^{log_6\:6 - log_6\:2}}\\\\\mathsf{6^{log_6\:\frac{6}{2}}}\\\\\mathsf{6^{log_6\:3} = 3}\end{array}}}$

$\Large\boxed{\begin{array}{I}\tt \mathsf{3^{-2 + log_3\:18}}\\\\\mathsf{3^{log_3\:3^{-2} + log_3\:18}}\\\\\mathsf{3^{log_3\:\frac{1}{9} + log_3\:18}}\\\\\mathsf{3^{log_3\:\frac{18}{9}}}\\\\\mathsf{3^{log_3\:2} = 2}\end{array}}}$

$\Large\boxed{\begin{array}{I}\tt \mathsf{5^{-log_5\:\frac{1}{3}}}\\\\\mathsf{5^{log_5\:\left(\frac{1}{3}\right)^{-1}}}\\\\\mathsf{5^{log_5\:3} = 3}\end{array}}}$

$\Large\boxed{\begin{array}{I}\tt \mathsf{4^{-\frac{1}{2} + 2\:log_2\:5}}\\\\\mathsf{4^{-\frac{1}{2} + \:log_2\:5^2}}\\\\\mathsf{4^{-\frac{1}{2} + \:log_2\:25}}\\\\\mathsf{4^{log_2\:2^{-\frac{1}{2}} + \:log_2\:25}}\\\\\mathsf{4^{log_2\:25.2^{-\frac{1}{2}}}\\\\\mathsf{2^{log_2\:\frac{625}{2}} = \frac{625}{2}}\end{array}}}$