Question

Solve for x: - 5^
x+1 +5^x-1 = 26. pls fast​

Answer 1

Answer:

STEP- BY- STEP explanation

5^1+x + 5^1-x=26

5×5^x+ 5×5^-x

$am + n = am \times n$

5×5^x+5×1/5x=26

5×5x+5/5x=26

5.5^2x-26.5+5=0

let

5x=y

5y^2-26+5=0

now it is a quadratic equation solve by factorisation:

5y^2-25y-y+5=0

5y(y-5)-1 (y-5)=0

(y-5) (5y-1)=0

so- y-5=0,y=5

now put the value of y

5x=y

5^x=5^1

x=-1 Ans

Answer 2

Answer:

5^1+x +5^1-x =26

5 × 5^x + 5× 5^-x =26

5×5x +5 × 1/5=26

(5 ×5^x5^x+5) /5^x=26

5 ×5^x5^x+5=26×5^x

(5×5^2x) -(26×5^x) +5=0

let 5^x = y

(5^x) ^2= y^2

5y^2 -26y +5=0

5y^2-25y-y+5=0

5y( y-5 ) -1( y-5 ) =0

(5y-1) (y-1) =0

y=5 , y=1/5

Now put the value of y in substitution

5^x=y or 5^x =1/5

5^x=5^1 or 5^x = 5 ^-1

x=1 or x = -1

Hope this helps you

Step-by-step explanation:

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