Question

1.dados log2 = 301 e log3 = 0,477 então log 14,4 Vale: (favor colocar o cálculo)

A) 1,328 B)1,158 C)1,238 D)1,248

​

Answer 1

Explicação passo-a-passo:

log 14,4

= log (144/10)

= log 144 - log 10

= log (2⁴ x 3²) - 1

= log 2⁴ + log 3² - 1

= 4.log 2 + 2.log 3 - 1

= 4.0,301 + 2.0,477 - 1

= 1,204 + 0,954 - 1

= 2,158 - 1

= 1,158

Letra B

Answer 2

$\displaystyle\sf{14,4=\frac{\diagdown\!\!\!\!\!\!\!\!\!144}{\diagup\!\!\!10}=\frac{72}{5}}\\\displaystyle\sf{log~14,4=log\left(\dfrac{72}{5}\right)}\\\sf{log\left(\dfrac{2^3\cdot3^2}{\frac{10}{2}}\right)}\\\sf{log2^3+log3^2-log10+log2}\\\sf{3log2+2log3-log10+log2=4log2+2log3-log10}\\\sf{log14,4=4\cdot0,301+2\cdot0,477-1}\\\sf{log14,4=1,204+0,954-1=1,158}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{\maltese~alternativa~b}}}}}$