Question

PFV É PRA AMANHÃ PRECISO URGENTE!

Calcule o valor de x em cada equação exponencial dada:
a) 2^x=4
b)2^x=8
c)10^x=1000
d)3^²x=27
e)49^x=7
f)(1/2)^x=1/16
g)(0,2)^⁴x=(0,2)¹⁶​

Answer 1

a) 2^x=4

${2}^{x} = 4$

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

$x = 2$

b)2^x=8

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

$x = 3$

c)10^x=1000

${10}^{x} = {10}^{3}$

$x = 3$

d)3^²x=27

${3}^{2x} = 27$

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

$2x = 3$

$x = \frac{3}{2} = 1.5$

e)49^x=7

${49}^{x} = {7}^{1}$

${( {7}^{2} )}^{x} = {7}^{1}$

${7}^{2x} = {7}^{1}$

$2x = 1$

$x = \frac{1}{2} = 0.5$

f)(1/2)^x=1/16

${( \frac{1}{2} )}^{x } = \frac{1}{16}$

${( \frac{1}{2} )}^{x} = \frac{ {1}^{4} }{ {2}^{4} }$

${( \frac{1}{2} )}^{x} = {( \frac{1}{2}) }^{4}$

$x = 4$

g)(0,2)^⁴x=(0,2)¹⁶

${0.2}^{4x} = {0.2}^{16}$

$4x = 16$

$x = \frac{16}{4}$

$x = 4$