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

...