Question

POR FAVORRRR PRECISO PRA AGORA ME AJUDEM A RESOLVER AS 3 QUESTOES / COM CALCULO POR FAVORRRRRRRRRRR

Answer 1

Explicação passo-a-passo:

1)

$\sf log~15=log~(3\cdot5)$

$\sf log~15=log~3+log~5$

$\sf \large\red{log~15=a+b}$

2)

$\sf \Rightarrow~log_{2}~32=x$

$\sf 2^x=32$

$\sf 2^x=2^5$

Igualando os expoentes:

$\sf x=5$

$\sf \Rightarrow~log_{4}~0,0625=y$

$\sf 4^y=0,0625$

$\sf 4^y=\dfrac{625}{10000}$

$\sf 4^y=\dfrac{1}{16}$

$\sf 4^y=\dfrac{1}{4^2}$

$\sf 4^y=4^{-2}$

Igualando os expoentes:

$\sf y=-2$

$\sf \Rightarrow~log_{2\sqrt{3}}~144=z$

$\sf (2\sqrt{3})^z=144$

$\sf (\sqrt{2^2\cdot3})^z=12^2$

$\sf (\sqrt{4\cdot3})^z=12^2$

$\sf (\sqrt{12})^z=12^2$

$\sf (12^{\frac{1}{2}})^z=12^2$

$\sf 12^{\frac{z}{2}}=12^2$

Igualando os expoentes:

$\sf \dfrac{z}{2}=2$

$\sf z=2\cdot2$

$\sf z=4$

Assim:

$\sf S=log_{2}~32+log_{4}~0,0625-log_{2\sqrt{3}}~144$

$\sf S=5+(-2)-4$

$\sf S=5-2-4$

$\sf S=3-4$

$\sf \large\red{S=-1}$

3)

$\sf log~2=log~\Big(\dfrac{10}{5}\Big)$

$\sf log~2=log~10-log~5$

$\sf \large\red{log~2=1-b}$