Evaluate - 3 x 2 - 7-2 x - 3-9 - 9 - 3 log 7 - x - 0

( 3 ^ x ^ 2 2x+3.9 9√( 3 ) #160; ) log( 7 x ) =0 ⇒ #160; either #160; ( 3 ^ x ^ 2 7.2x+3.9 9√( 3 ) #160; ) =0 or, #160; #160; ...

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Standard IX

Mathematics

Logarithms

Evaluate : ...

Question

Evaluate : $(3^{x^{2} - 7.2 x + 3.9} - 9 \sqrt{3}) log (7 - x) = 0$

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Solution

$(3^{x^{2} - 2 x + 3.9} - 9 \sqrt{3}) l o g (7 - x) = 0$
$\Rightarrow$ either $(3^{x^{2} - 7.2 x + 3.9} - 9 \sqrt{3}) = 0$
or, $L o g (7 - x) = 0$
Case (i) $l o g (7 - x) = 0$
$\Rightarrow x = 6$
Case (ii) $3^{x^{2} - 7.2 x + 3.9} - 9 \sqrt{3} = 0$
$\Rightarrow x^{2} - 7.2 x + 3.9 = 2.5$
$\Rightarrow x^{2} - 7.2 x + 1.4 = 0$
$\Rightarrow x = 0.2$ or $x = 7$
if $x = 7$ , $l o g (7 - x)$ does not exist
$∴$ $x = 6$ or $x = 0.2$

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Similar questions

Q. Solve the following equations.

(3^{x^{2} - 7.2 x + 3.9} - 9 \sqrt{3}) log (7 - x) = 0

Q. If

x_{1}

and

x_{2} (x_{1} > x_{2})

are the roots of the equation

\sqrt{(6 - x)} (3^{x^{2} - 7.2 x + 3.9} - 9 \sqrt{3}) = 0

then calculate

x_{1} - \frac{1}{x_{2}}

Evaluate ${lim}_{x \to 3} \frac{x^{2} - 9}{x - 3}$

The solution set of the inequality
$\sqrt{6 - x} (5^{x^{2} - 7.2 x + 3.9} - 25 \sqrt{2}) \geq 0$ can be given by $(- a, \frac{b}{c})$ , then c - b = ___

Evaluate (i) $l i m x \to 3 (\frac{x^{2} - 9}{x - 3})$

(ii) $l i m x \to 1 (\frac{(x^{2} - 4 x + 3)}{x - 1})$

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Evaluate : (3x2−7.2x+3.9−9√3)log(7−x)=0

(3x2−2x+3.9−9√3)log(7−x)=0⇒ either (3x2−7.2x+3.9−9√3)=0or, Log(7−x)=0Case (i) log(7−x)=0 ⇒x=6Case (ii) 3x2−7.2x+3.9−9√3=0⇒x2−7.2x+3.9=2.5⇒x2−7.2x+1.4=0⇒x=0.2 or x=7if x=7, log(7−x) does not exist ∴ x=6 or x=0.2

Evaluate : $(3^{x^{2} - 7.2 x + 3.9} - 9 \sqrt{3}) log (7 - x) = 0$