3-x-1-2-x-faind-x-

Question Number 167248 by mathlove last updated on 10/Mar/22

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

Commented by mr W last updated on 10/Mar/22

3^{\frac{x}{2}} + 1 = 2^{x}

3 + 1 = 2^{2}

\Rightarrow x = 2

Answered by LEKOUMA last updated on 10/Mar/22

3^{\frac{1}{2} x} + 1 = 2^{x}

\Leftrightarrow \ln (3^{\frac{1}{2} x} + 1) = \ln (2^{x})

\Leftrightarrow \ln (3^{\frac{1}{2} x}) + \ln (1) = \ln (2^{x})

\Leftrightarrow \ln 3^{\frac{1}{2} x} + \ln 1 = \ln 2^{x}, o r \ln 1 = 0

\Leftrightarrow \frac{1}{2} x \ln 3 = x \ln 2

\Leftrightarrow x \ln 3 = 2 x \ln 2

\Leftrightarrow x \ln 3 - 2 x \ln 2 = 0

\Leftrightarrow x (\ln 3 - 2 \ln 2) = 0

\Leftrightarrow x = \frac{0}{\ln 3 - 2 \ln 2} = 0

x = 0

Commented by mr W last updated on 10/Mar/22

i f x = 0, t h e n

1 + 1 = 1

Commented by mr W last updated on 10/Mar/22

w h e r e h a v e y o u l e a r n t

\ln (a + b) = \ln a + \ln b ?

Commented by LEKOUMA last updated on 10/Mar/22

o k

Answered by HeferH last updated on 10/Mar/22

3^{\frac{x}{2}} + 1 = 2^{x}

1 = 2^{x} - 3^{\frac{x}{2}}

2^{2} - 3^{1} = 2^{x} - 3^{\frac{x}{2}}

t h e n : x = 2

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