Explicație pas cu pas:
a)
(2x)² = 64
4x² = 64 |:4
x² = 16
x² = 4² => x = ±4
b)
(5x)² = 25³
25x² = 25³ |:25
x² = 25² => x = ±25
d)
[tex]{10}^{x + 2} = {( {2}^{2} \cdot {5}^{2} )}^{2} \\ {10}^{x + 2} = {( {(2\cdot 5)}^{2} )}^{2}[/tex]
[tex]{10}^{x + 2} = {({10}^{2} )}^{2}[/tex]
[tex]{10}^{x + 2} = {10}^{4}[/tex]
[tex]x + 2 = 4 \implies x = 2[/tex]
e)
[tex]3 + {3}^{x + 1} = 30[/tex]
[tex]{3}^{x + 1} = 27[/tex]
[tex]{3}^{x + 1} = {3}^{3} [/tex]
[tex]x + 1 = 3 \implies x = 2[/tex]
f)
[tex]{2}^{x} + {2}^{x + 1} + {2}^{x + 2} = 112 \\ {2}^{x} \cdot ( {2}^{0} + {2}^{1} + {2}^{2} ) = 112[/tex]
[tex]{2}^{x} \cdot (1 + 2 + 4) = 112[/tex]
[tex]7 \cdot {2}^{x} = 112 \iff {2}^{x} = 16[/tex]
[tex]{2}^{x} = {2}^{4} \implies x = 4[/tex]
