Respostas
Resposta:
Ola!
\begin{gathered}a) {25}^{x} = 3125 \\ {( {5}^{2} )}^{x} = {5}^{5} \\ {5}^{2x} = {5}^{5} \\ 2x = 5 \\x = \frac{5}{2} \end{gathered}
a)25
x
=3125
(5
2
)
x
=5
5
5
2x
=5
5
2x=5
x=
2
5
\begin{gathered}b) {27}^{x} = 243 \\ { ({3}^{3}) }^{x} = {3}^{5} \\ {3}^{3x} = {3}^{5} \\ 3x = 5 \\ x = \frac{5}{3} \end{gathered}
b)27
x
=243
(3
3
)
x
=3
5
3
3x
=3
5
3x=5
x=
3
5
\begin{gathered}c) { \frac{1}{2} }^{x} = \frac{1}{512} \\ {2}^{ - x} = \frac{1}{ {2}^{9} } \\ {2}^{ - x} = {2}^{ - 9} \\ - x = - 9.( - 1) \\ x = 9\end{gathered}
c)
2
1
x
=
512
1
2
−x
=
2
9
1
2
−x
=2
−9
−x=−9.(−1)
x=9
\begin{gathered}d) { \frac{3}{5} }^{2x} = \frac{81}{625} \\ { \frac{3}{5} }^{2x} = { \frac{3}{5} }^{4} \\ 2x = 4 \\ x = \frac{4}{2} \\ x = 2\end{gathered}
d)
5
3
2x
=
625
81
5
3
2x
=
5
3
4
2x=4
x=
2
4
x=2
\begin{gathered}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} \end{gathered}
e)
4
1
4x
=0.5
(
2
2
1
)
4x
=0.5
2
1
8x
=
2
1
8x=1
x=
8
1
\begin{gathered}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} \end{gathered}
f)4
x
=
3
128
(2
2
)
x
=
3
2
7
2
2x
=2
3
7
2x=
3
7
6x=7
x=
6
7
\begin{gathered}g) {10}^{3x} = \frac{1}{1000} \\ {10}^{3x} = {10}^{ - 3} \\ 3x = - 3 \\ x = \frac{ - 3}{3} \\ x = - 1\end{gathered}
g)10
3x
=
1000
1
10
3x
=10
−3
3x=−3
x=
3
−3
x=−1
\begin{gathered}h)10 \times {3}^{x - 3} = 90 \\ {3}^{x - 3} = 9 \\ {3}^{x - 3} = {3}^{2} \\ x - 3 = 2 \\ x = 2 + 3 \\ x = 5\end{gathered}
h)10×3
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!!