Răspuns:
Explicație pas cu pas:
a)
( 3ˣ)⁵ = 3¹⁰ x 3⁵
3⁵ˣ = 3⁽¹⁰⁺⁵⁾
3⁵ˣ = 3¹⁵ => 5 x = 15 => x = 15 : 5 => x = 3
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b)
x + ( 2²)⁵ =2³ x 2⁷
x + 2²ˣ⁵ = 2³⁺⁷
x + 2¹⁰ = 2¹⁰
x = 2¹⁰ - 2¹⁰
x = 0
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c)
5³ x 6 + 5⁴ x 7 = 5³ x ( 6 + 5 x 7 ) = 5³ x 41 = 125 x 41 = 5 125
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d)
x² + x³ + x⁴ = x² ( 1 + x + x²)
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e)
3ˣ + 3ˣ⁻¹ = 4
3ˣ( 1 + 3⁻1) = 4
3ˣ ( 3/3 + 1/3) = 4
3ˣ x (4/3 ) = 4
3ˣ = 4 : (4/3)
3ˣ = 4 x ( 3/4)
3ˣ = 3¹ => x = 1
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f)
5 x 3ˣ - 2 x 3ˣ = 81
3ˣ x ( 5 - 2 ) = 81
3ˣ x 3 = 81
3ˣ = 81 : 3
3ˣ = 27
3ˣ = 3³ => x = 3
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g)
3²ˣ⁺¹ - 3²ˣ - 3²ˣ⁻¹ - 3²ˣ⁻² - 3²ˣ⁻³ = 123
3²ˣ x ( 3¹ - 1 - 3⁻¹ - 3⁻² - 3⁻³ ) = 123
3²ˣ x ( 2 - 1/3 - 1/3² - 1/3³ ) = 123
3²ˣ x ( 54/27 - 9/27 - 3/27 - 1/27 ) = 123
3²ˣ x ( 41/27 ) = 123
3²ˣ = 123 : ( 41/27 )
3²ˣ = 123 x ( 27/41)
3²ˣ = 3 x 3³
3²ˣ = 3¹⁺³
3²ˣ = 3⁴ => 2 x = 4 => x = 4 : 2 => x = 2
