Question

$\mathtt{ \red{ \large{Question}}}$
$3 {}^{2x - 2} - 5 \times 3 {}^{x - 2} - 66 = 0$
Find the value of "x"

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Answer 1

$\large{\dag{\underline{\underline{\sf{\pmb{Given \: Equation}}}}}}$

$\sf{\rightarrow{3 {}^{2x - 2} - 5 \times 3 {}^{x - 2} - 66 = 0}}$

$\\\large{\dag{\underline{\underline{\sf{\pmb{To \: Find: - }}}}}}$

$\sf{\rightarrow{ The \: value \: of \: \bold{x}}}$

$\\\large{\dag{\underline{\underline{\sf{\pmb{Solution: - }}}}}}$

$\\ \sf{\bold{3 {}^{2x - 2} - 5 \times 3 {}^{x - 2} - 66 = 0}}$

$\\ \sf{\implies{ {3}^{2x} \times {3}^{ - 2} - 5 \times {3}^{x} \times {3}^{ - 2} - 66 = 0}}$

$\\ \sf{\implies{ {3}^{2x} \times \dfrac{1}{9} - 5 \times {3}^{x} \times \dfrac{1}{9} - 66 = 0}}$

$\\ \sf{\implies{ \dfrac{3 {}^{2x} }{9} - \dfrac{5}{9} \times {3}^{x} - 66 = 0}}$

$\\ \sf{\implies{ {3}^{2x} - 5 \times {3}^{x} - 594 = 0}} \: \: \: \: \: \: \: \: \: \: \boxed{\sf{Multiplying \: by \: 9}}$

$\\ \sf{\implies{ {a}^{2} - 5a - 594 = 0}} \: \: \: \: \: \: \: \: \: \boxed{\sf{Let \: {3}^{x} \: be \: a}}$

$\\ \sf{\implies{ {a}^{2} - 27a + 22a - 594 = 0}}$

$\\ \sf{\implies{a(a - 27) + 22(a - 27) = 0}}$

$\\ \sf{\implies{(a - 27)(a + 22) = 0}}$

Now, either (a-27)=0 or (a+22)=0

$\\\sf{But \: a \: \cancel{ = }\: 22 \: because \:a = {3}^{x} > 0 \: hence, a + 22\: \cancel{ = } \: 0}$

Therefore,

$\\ \sf{a - 27 = 0}$

$\\ \sf{\implies{ {3}^{x} = 27}}$

$\\ \sf{\implies{ {3}^{x} = {3}^{3}}}$

Now, as the base are same, we can write:-

$\\ \sf{\therefore{\bold{\red{x = 3}}}}$

$\\ \underline{\boxed{\rm{Hence, \: the \: value \: of \: x = \bold{3}}}}$

Answer 2

Step-by-step explanation:

Thanks nuha sis

for giving me multiple thanks

ha

well

can you tell me how you able to give me multiple thanks in such a manner

when I try almost my maximum number of multiple thanks is 2

but some time it go over 18

thanks nuha sis