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4 éve
a,
`7^(2x-1)` = `9^(4x-2)` = `81^(2x-1)`
2x-1 = 0
2x = 1
x = `1/2`
b,
`(1/16)^(4-2|x-3|)` = 256
`2^(-4*(4-2|x-3|))` = `2^8`
-16+8|x-3| = 8
8|x-3| = 24
|x-3| = 3
`x_1` = 6
`x_2` = 0
c,
`0.5^(x^2+2x-35)` = 1
`x^2`+2x-35 = 0
`(x-5)(x+7)` = 0
`x_1` = 5
`x_2` = -7
d,
`16^(|x|-2)` = 4 = `16^(1/2)`
|x|-2 = `1/2`
|x|= `5/2`
`x_1` = `5/2`
`x_2` = `-5/2`
e,
`(5/3)^(3x+7)` = `(9/25)^(x-3)` = `(3/5)^(2(x-3))` = `(5/3)^(-2(x-3))`
3x+7 = -2(x-3)
3x+7 = -2x+6
5x = -1
x = `-1/5`
f,
`100^x` = 0,000001
`(10^2)^x` = `10^(-6)`
`10^(2x)` = `10^(-6)`
2x = -6
x = -3
g,
`49^x` = -7
Egy pozitív szám akárhanyadik hatványa pozitív, nincs megoldás.
h,
`(1/0.3)^(4+3x)` = `(100/9)^x`
`(10/3)^(4+3x)` = `((10/3)^2)^x` = `(10/3)^(2x)`
4+3x = 2x
x = -4
i,
`7^(2-4x)` = `1/(49^(7+6x))` = `7^(-2(7+6x))`
2-4x = -2(7+6x)
2-4x = -14-12x
8x = -16
x = -2
Módosítva: 4 éve
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