Logaritmos

TRABAJO GRUPAL

(8^(X^2-4) )^(1/(X+2))= (4^((X-2)/2) )^(1/(X+2))

8^(X^2-4)=4^((X-2)/2)

2^(〖3(X〗^2-4))=2^2((X-2)/2)

De aquí: Se igualan los exponentes

〖3(X〗^2-4) = 2((X-2)/2)

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

3= 1/((x+2) )

3(x+2)=1

3x+6=1

3x= 1/6

x= (-5)/3

(27/8)^(x^2-1/3) (3/2)^(-3-2x)= (4/9)^(x^2-3x)

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

〖(3/2)^3(x^2-1/3) (3/2)^(- (2x+3))= 〗^ (2/3)^(〖2(x〗^2-3x))

〖(2/3)^(-3(x^2-1/3) ) (2/3)^( (2x+3) )= 〗^ (2/3)^(〖2(x〗^2-3x))

〖〖 (2/3)〗^(1-〖3x〗^2 ) (2/3)^( (2x+3) )= 〗^ (2/3)^(〖2x〗^2-6x))

〖〖 (2/3)〗^(2x-〖3x〗^2+4) = 〗^ (2/3)^(〖2x〗^2-6x))

2x-3x^2+4= 〖2x〗^2-6x

4= 〖5x〗^2-8x

x=2

5^((5x+1)/9) › (125)^((x+1)/10)

5^((5x+1)/9) › 5^3((x+1)/10)

(5x+1)/9 › 3((x+1)/10)

(5x+1)/9- 3((x+1)/10) › 0

(10x+10-27x27)/90 › 0

(23x-17)/90 › 0

23x › 17

x › 17/23

log_3⁡x-3 log_x⁡3+ 1/4 log_3⁡x= log⁡10

5/4 log_3⁡x- 3/log_3⁡x =1

(5/4 〖(log_3⁡x)〗^2-3)/log_3⁡x =1

(5〖(log_3⁡x)〗^2-12)/(4 log_3⁡x )=1

5〖(log_3⁡x)〗^2-12= 4 log_3⁡x

5〖(log_3⁡x)〗^2-4 log_3⁡〖x-12〗=0

5 log_3⁡x +6

1 log_3⁡x -2

(5 log_3⁡x+6)(log_3⁡x-1)=0

log_3⁡x= (-6)/5 v log_3⁡x=1

x= 3^((-6)/5) v x=3

(log_5⁡〖x 〗+ log_x⁡5)/(1+ log_5⁡x )= 17/20

(((log_5⁡〖x 〗 )^2+ 1)/( log_5⁡x ))/(1+ log_5⁡x )= 17/20

((log_5⁡〖x 〗 )^2+ 1)/( log_5⁡x+ (log_5⁡〖x 〗 )^2 )= 17/20

20(log_5⁡〖x 〗 )^2+20= 17 log_5⁡x+ 〖17(log_5⁡〖x 〗 )〗^2

3(log_5⁡〖x 〗 )^2 - 17 log_5⁡x+20=0

3 log_5⁡x -5

〖1log〗_5⁡x -4

(3 log_5⁡x-4)(log_5⁡〖x-5)=0〗

log_5⁡x= 5/3 log_5⁡x=4

x=5^(5/3) x=625

(log_2⁡x ) (log_(x/2)⁡2 )+log_(x/16)⁡2=0

log_2⁡x/log_2⁡〖x/2〗 +log_(x/16)⁡2=0

log_2⁡〖x/(x/2)〗+log_(x/16)⁡2=0

log_2⁡2+ log_(x/16)⁡2=0

〖 log〗_(x/16)⁡2=

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