Question

1) Calcule o valor do logarítmo

(a) log3 81

(b) log6 1296

(c) log2 √ 2

(d) log 100

(e) log2 1024

(f) logπ π

(g) log 1/ 2 8

(h) log 1/ 2 32

(i) log27 81

(j) log√ 8 √ 32

Answer 1

Resposta:

a) log3 81

${3}^{x} = 81$

${3}^{x} = {3}^{4} =$

corta-se a base fica

$x = 4$

(b) log6 1296

6^x = 1296

6^x=6^4

x=4

(c) log2 √ 2

log2 √ 2 =x

${2}^{x} = \sqrt{2}$

${2}^{x} = {2}^{1)2} =$

$x = \frac{1}{2}$

(d) log 100

qd a base não aparece será sempre 10

${10}^{x} = 100$

${10}^{x} = {10}^{2}$

$x = 2$

(e) log2 1024

log2 1024 =x

${2}^{x} = {2}^{10}$

$x = 10$

(f) logπ π

logπ π= x

π =π^x

x=1

(g) log 1/ 2 8

log 1/ 2 8 =x

${8}^{x} = \frac{1}{2}$

${2}^{3 = {2}^{ - 1} }$

$3x = - 1$

$x = - \frac{1}{3}$

(h) log 1/ 2 32

log 1/ 2 32 =x

${32}^{x} = \frac{1}{2}$

${2}^{5} = {2}^{ - 1}$

$5x = - 1$

$x = - \frac{1}{5}$

(i) log27 81

log27 81 =x

${27}^{x} = 81$

${3}^{3x} = {3}^{4}$

$3x = 4$

$x = \frac{4}{3}$

(j) log√ 8 √ 32

log√ 8 √ 32=x

${8}^{x} = 32$

${2}^{3x} = {2}^{5}$

$3x = 5$

$x = \frac{5}{3}$