Question

Easy question this time!!

$\: \: \: \: \: \:$
Find value of x :
$\sf {6}^{3x} + 4 - 216 = 35 \times {6}^{3x} + 2$

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Answer 1

$\large\underline{\sf{Solution-}}$

Given equation is

$\rm :\longmapsto\:{6}^{3x} + 4 - 216 = 35 \times {6}^{3x} + 2$

Let assume that

$\rm :\longmapsto\:\boxed{\tt{ {6}^{3x} = y}}$

So, above equation can be rewritten as

$\rm :\longmapsto\:y - 216 + 4 = 35 \times y + 2$

$\rm :\longmapsto\:y - 212 = 35y + 2$

$\rm :\longmapsto\:y - 35y = 212 + 2$

$\rm :\longmapsto\: - 34y = 214$

$\sf\implies \: y \: = \: - \: \dfrac{214}{34}$

$\sf\implies \: {6}^{3x} \: = \: - \: \dfrac{214}{34}$

We know,

$\rm :\longmapsto\:\boxed{\tt{ \: {6}^{3x} > 0 \: }}$

$\bf\implies \:There \: is \: no \: real \: value \: of \: x$

Hence,

$\boxed{\tt{ \:{6}^{3x} + 4 - 216 = 35 \times {6}^{3x} + 2 \: has \: no \: solution \: }}$

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MORE TO KNOW

$\begin{gathered}(1)\:{\underline{\boxed{\bf{\blue{a^m\times{a^n}\:=\:a^{m\:+\:n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(2)\:{\underline{\boxed{\bf{\green{a^m\div{a^n}\:=\:a^{m\: - \:n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(3)\:{\underline{\boxed{\bf{\orange{\dfrac{1}{x^n}\:=\:x^{-n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(4)\:{\underline{\boxed{\bf{\red{\:x^{0}\: = \: 1 \: }}}}} \\ \end{gathered}$

Answer 2

$There \: is \: no \: real \: value \: of \: x \\ </p><p></p><p>so \\ </p><p></p><p>\boxed{\tt{ \:{6}^{3x} + 4 - 216 = 35 \times {6}^{3x} + 2 \: has \: no \: solution \: }}</p><p></p><p>$