Question

1) Resolva as equações exponenciais:

a)25^x = 3125
b)27^x = 243
c)(1/2)^x = 1/512
d)(3/5)^ 2x = 81/625
e)(1/4) ^ 4x = 0,5
f) 4x = ∛128
g)10^3x = 1/1000
h)10 * 3^x-3 = 90

Answer 1

Ola!

$a) {25}^{x} = 3125 \\ {( {5}^{2} )}^{x} = {5}^{5} \\ {5}^{2x} = {5}^{5} \\ 2x = 5 \\x = \frac{5}{2}$

$b) {27}^{x} = 243 \\ { ({3}^{3}) }^{x} = {3}^{5} \\ {3}^{3x} = {3}^{5} \\ 3x = 5 \\ x = \frac{5}{3}$

$c) { \frac{1}{2} }^{x} = \frac{1}{512} \\ {2}^{ - x} = \frac{1}{ {2}^{9} } \\ {2}^{ - x} = {2}^{ - 9} \\ - x = - 9.( - 1) \\ x = 9$

$d) { \frac{3}{5} }^{2x} = \frac{81}{625} \\ { \frac{3}{5} }^{2x} = { \frac{3}{5} }^{4} \\ 2x = 4 \\ x = \frac{4}{2} \\ x = 2$

$e) { \frac{1}{4} }^{4x} = 0.5 \\ ({ \frac{1}{ {2}^{2} }) }^{4x} = 0.5 \\ { \frac{1}{2} }^{8x} = \frac{1}{2} \\ 8x = 1 \\ x = \frac{1}{8}$

$f) {4}^{x} = \sqrt[3]{128} \\ {( {2}^{2} )}^{x} = \sqrt[ 3 ]{ {2}^{7} } \\ {2}^{2x} = {2}^{ \frac{7}{3} } \\ 2x = \frac{7}{3} \\ 6x = 7 \\ x = \frac{7}{6}$

$g) {10}^{3x} = \frac{1}{1000} \\ {10}^{3x} = {10}^{ - 3} \\ 3x = - 3 \\ x = \frac{ - 3}{3} \\ x = - 1$

$h)10 \times {3}^{x - 3} = 90 \\ {3}^{x - 3} = 9 \\ {3}^{x - 3} = {3}^{2} \\ x - 3 = 2 \\ x = 2 + 3 \\ x = 5$

Espero ter ajudado. Bons estudos!!