Question

1- Sendo log 2 = x, calcular log50.

2- Sendo log$(27/10) = k$, ache log3

3- Sendo log(a+b) = m e a-b = 100, calcule o log $(a^2-b^2)$ wm função de m.

Answer 1

$1- \\\\\ell og(2)=x\\\ell og(50)=y\\\\\ell og(\frac{100}{2})=y\\\\\ell og(100)-\ell og(2)=y\\\\\boxed{\ell og(50) =2-x}$

$2-\\\\\ell og(\frac{27}{10})=k\\\ell og(3)=x\\\\\\\ell og(\frac{3^3}{10})=k\\\\3.\ell og(3)-\ell og(10)=k\\\\3.\ell og(3)-1=k\\\\\boxed{\ell og(3)=\dfrac{k+1}{3}}$

$3-\\\\\ell og(a+b)=m\\a-b=100\\\ell og(a^2-b^2)=x\\\\\\a-b=100~\cdot~(a+b)\\\\a^2-b^2=100.(a+b)\\\\\ell og(a^2-b^2)=\ell og(100.[a+b])\\\\\ell og(a^2-b^2)=\ell og(100)+\ell og(a+b)\\\\\boxed{\ell og(a^2-b^2)=2+m}$

Dúvidas? comente