Question

if 5^x-1 + 5^x+1=650 then find x​

Answer 1

Answer:

The value of x is 3

Step-by-step explanation:

Given:

$\bf\,5^{x-1}+5^{x+1}=650$

$\implies\,5^x\,5^{-1}+5^x\,5=650$

$\implies\,5^x\,\frac{1}{5}+5^x\,5=650$

$\implies\,5^x(\frac{1}{5}+5)=650$

$\implies\,5^x(\frac{1+25}{5})=650$

$\implies\,5^x(\frac{26}{5})=650$

$\implies\,5^x=650\times\frac{5}{26}$

$\implies\,5^x=25\times\,5$

$\implies\,5^x=5^3$

Equating powers on both sides, we get

$\boxed{\bf\,x=3}$

Answer 2

Answer:-

5^x-1 + 5^x+1 = 650

{Take 5^x common}

5^x(5^-1 + 5^+1)

5^x(1/5 + 5)

5^x(25+1/5)

5^x(26/5)

5^x=650*5/26 [650/26=25]

5^x=25*5

5^x=5*5*5

5^x=5^3. [Bases are same]

x=3

Hence,value of x=3.....

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