3-x-1-2-x-find-x-

Question Number 202116 by Calculusboy last updated on 21/Dec/23

\sqrt{3^{\boldsymbol x}} + 1 = 2^{\boldsymbol x} \boldsymbol f i n d \boldsymbol x

Answered by Frix last updated on 21/Dec/23

Obviously x = 2

\sqrt{3^{2}} + 1 = \sqrt{9} + 1 = 3 + 1 = 4 = 2^{2}

Commented by Calculusboy last updated on 21/Dec/23

\boldsymbol t h a n k s, \boldsymbol b u t \boldsymbol s i r \boldsymbol c a n \boldsymbol i \boldsymbol g e t \boldsymbol s o l u t i o n \boldsymbol f o r \boldsymbol i t

Answered by MATHEMATICSAM last updated on 22/Dec/23

\sqrt{3^{\boldsymbol x}} + 1 = 2^{\boldsymbol x} \boldsymbol f i n d \boldsymbol x

let f (x) = \sqrt{3^{x}} + 1 - 2^{x}

f (2) = \sqrt{3^{2}} + 1 - 2^{2} = 3 + 1 - 4 = 0

As f (2) = 0 so that we can say x = 2

Commented by Calculusboy last updated on 23/Dec/23

\boldsymbol t h a n k s \boldsymbol s i r

Commented by Frix last updated on 23/Dec/23

This is not a solution method .

Try \sqrt{5^{x}} + 1 = 3^{x}

You can only approximate .

\sqrt{3^{x}} + 1 = 2^{x} is constructed to have the

obvious solution x = 2 . The principle is

a + b = c^{n} \Rightarrow \sqrt[n]{a^{n}} + b = c^{n}

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