Question

If 5^x+1 + 5^x-1 =650 then find x​

Answer 1

❏ Formula Used:-

❚➾ Index Formula

$\sf\longrightarrow X{}^{m}\times X{}^{n}=X{}^{m+n}$

$\sf\longrightarrow \frac{X{}^{m}} {X{}^{n}}=X{}^{m-n}\:\: or\:\:=\frac{1}{X{}^{n-m}}$

$\sf\longrightarrow X{}^{m}\times Y{}^{m}={XY}^{m}$

$\sf\longrightarrow\frac{ X{}^{m}}{Y{}^{m}}=(\frac{X}{Y}){}^{m}$

❏ Question:-

Q) Find the value of x, if;

$\sf\longrightarrow 5{}^{x+1}+5{}^{x-1}=650$

❏ Solution:-

❚➾ $\sf\longrightarrow 5{}^{x+1}+5{}^{x-1}=650$

$\sf\longrightarrow 5{}^{x}\times5{}^{1}+\frac{5{}^{x}}{5{}^{1}}=650$

$\sf\longrightarrow 5{}^{x}\times(5+\frac{1}{5})=650$

$\sf\longrightarrow 5{}^{x}\times(\frac{25+1}{5})=650$

$\sf\longrightarrow 5{}^{x}\times(\frac{26}{5})=650$

$\sf\longrightarrow 5{}^{x}=\cancel{650}\times\frac{5}{\cancel{26}}$

$\sf\longrightarrow 5{}^{x}=25\times5$

$\sf\longrightarrow 5{}^{x}=5{}^{2}\times5{}^{1}$

$\sf\longrightarrow 5{}^{x}=5{}^{2+1}$

$\sf\longrightarrow 5{}^{x}=5{}^{3}$

[ comparing both sides ]

$\sf\longrightarrow \boxed{\red{\large{x=3}}}$

∴ The value of x is 3

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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