a,

`2^(4x-3)=4`

`2^(4x-3)=2^2`

Az alapok egyenlők, a kitevők is.

`4x-3=2` /+3

`4x=5` /:4

`color(red)(x=5/4)`

Ellenőrzés:

`2^(4*5/4-3)=4`

`2^2=4`

4=4

b,

`3^(3-2x)=27`

`3^(3-2x)=3^3`

`3-2x=3` /-3

`-2x=0` /:(-2)

`color(red)("x = 0")`

Az ellenőrzéseket megyhagyom neked.

c,

`4^(4x-1)=1/16`

`4^(4x-1)=4^(-2)`

`4x-1=-2` /+1

`4x=-1` /:4

`color(red)(x=-1/4)`

d,

`5^(8x-7)=1/125`

`5^(8x-7)=5^(-3)`

`8x-7=-3` /+7

`8x=4` /:8

`color(red)(x=1/2)`

e,

`2^(x-3)*2^x=16`

`2^(x-3+x)=2^4`

`2x-3=4` /+3

`2x=7` /:2

`color(red)(x=7/2)`

f,

`3^x*3^(2x-1)=9`

`3^(x+2x-1)=3^2`

`3x-1=2` /+1

`3x=3` /:3

`color(red)(x=1)`

g,

`5^(2x+3)*25=5^(3x-4)`

`5^(2x+3+2)=5^(3x-4)`

`2x+5=3x-4` /+4

`2x+9=3x` /-2x

`color(red)(x=9)`

h,

`49^x*7^(x-3)=7^(4x-5)`

`7^2*7^(x-3)=7^(4x-5)`

`7^(2+x-3)=7^(4x-5)`

`x-1=4x-5` /+5

`x+4=4x` /-x

`3x=4` /:3

`color(red)(x=4/3)`

i,

`2^(3x+5)/2^x=1/8`

`2^(3x+5-x)=2^(-3)`

`2x+5=-3` /-5

`2x=-8` /:2

`color(red)(x=-4)`

j,

`3^(x-2)/3^(2x+3)=1/81`

`3^(x-2-(2x+3))=3^(-4)`

`-x-5=-4` /+5

`-x=1`

`color(red)(x=-1)`

k,

`11^(4x-1)/121^(x+1)=11^(x-3)`

`11^(4x-1-2(x+1))=11^(x-3)`

`4x-1-2x-2=x-3`

`2x-3=x-3` /+3

`2x=x` /-x

`color(red)(x=0)`

l,

`125^(x+2)/25^(x+1)=5^(3x-6)`

`5^(3(x+2)-2(x+1))=5^(3x-6)`

`3(x+2)-2(x+1)=3x-6`

`3x+6-2x-2=3x-6`

`x+4=3x-6` /-x

`2x-6=4` /+6

`2x=10` /:2

`color(red)(x=5)`

m,

`root()(2^(x+5))=4^2`

`2^((x+5)/2)=2^4`

`(x+5)/2=4` /`*2`

`x+5=8` /-5

`color(red)(x=3)`

n,

`root(3)(3^(x-1))=1/9`

`3^((x-1)/3)=3^(-2)`

`(x-1)/3=-2` /`*3`

`x-1=-6` /+1

`color(red)(x=-5)`

o,

`root(4)(4^(2x-1))=64`

`4^((2x-1)/4)=4^3`

`(2x-1)/4=3` /`*4`

`2x-1=12` /+1

`2x=13` /:2

`color(red)(x=13/2)`

p,

`root(6)(5^(5x+2))=25^(1/4)`

`5^((5x+2)/6)=5^(1/2)`

`(5x+2)/6=1/2` /`*6`

`5x+2=3` /-2

`5x=1` /:5

`color(red)(x=1/5)`

q,

`13^(2x-7)=1`

Hányadik hatvány 1? nulladik.

`2x-7=0` /+7

`2x=7` /:2

`color(red)(x=7/2)`

r,

`7^(2x+5)-1=0` /+1

`7^(2x+5)=1`

nulladik hatvány lesz 1.

`2x+5=0` /-5

`2x=-5` /:2

`color(red)(x=-5/2)`.