Question

Ajuda ? é sobre logaritmo 

Answer 1

a) $log\ \frac{1}{8}\ 4=x\\\\ (\frac{1}{8})^x = 4\\\\ 2^-^3^x =2^2\\\\ -3x=2\\\\ \boxed{x=-\frac{2}{3}}$

b) $log\ _2_7\ \sqrt{3}=x\\\\ 27^x=\sqrt{3}\\\\ 3^3^x = 3^\frac{1}{2}\\\\ 3x=\frac{1}{2}\\\\ \boxed{x=\frac{1}{6}}$

c) $log\ _1_6\ 0,125=x\\\\ 16^x=\frac{1}{8}\\\\ 2^4^x=2^-^3\\\\ 4x=-3\\\\ \boxed{x=-\frac{3}{4}}$

d) $log\ \sqrt[3]{100}=x\\\\ 10^x=10^\frac{2}{3}\\\\ \boxed{x=\frac{2}{3}}$

e) $log\ _3\ x=-2\\\\ 3^-^2=x\\\\ \boxed{x=\frac{1}{9}}$

f) $log\ _\frac{1}{2}\ x=3\\\\ (\frac{1}{2})^3=x\\\\ \boxed{x=\frac{1}{8}}$

g) $log\ _x\ \frac{1}{4}=-1\\\\ x^-^1=\frac{1}{4}\\\\ x^-^1 = 4^-^1\\\\ \boxed{x=4}$

h) $log\ _x\ 32=10\\\\ x^1^0 = 32\\\\ x^1^0=2^5\\\\ x^5^(^2^) = 2^5\\\\ x^2=2\\\\ \boxed{x=\sqrt{2}}$