Question

answer me plz guys plz​

Answer 1

$\underline{\text{Solution :}}$

$\mathrm{Given,\:3^{x}-3^{x-1}=18}$

$\implies \mathrm{3^{x}-3^{x}*3^{-1}=18}$

$\implies \mathrm{3^{x}(1 - 3^{-1})=18}$

$\implies 3^{x}(1-\frac{1}{3})=18$

$\implies \mathrm{3^{x}*\frac{3-1}{3}=18}$

$\implies \mathrm{3^{x}*\frac{2}{3}=18}$

$\implies \mathrm{3^{x}=18*\frac{3}{2}}$

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

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

$\implies \mathrm{x=3}$

$\therefore \boxed{\mathrm{2^{x}=2^{3}=8}}$

$\underline{\text{Laws of indices :}}$

$\mathrm{1.\:a^{m}\times a^{n}=a^{m+n}}$

$\mathrm{2.\:a^{-1}=\frac{1}{a}}$

$\mathrm{3.\:(a^{m})^{n}= a^{mn}}$

$\mathrm{4.\:a^{\frac{m}{n}}=\sqrt[n]{a^{m}}}$

$\mathrm{5.\:a^{m}\times b^{m}=(a\times b)^{m}}$

Answer 2

ANSWER:---------

3 x−3 x∗3 −1=18

⟹3x(1−3−1)=1)8( 3^{x}(1 - 3^{-1})=18⟹3 )



(1−3 −1)=18

3x(1−13)=18. (3^{x}(1-\frac{1}{3})=183 )

3x3−13=18\implies 3^{x}\:\frac{3-1}{3}=183



33−1=18

3x23=18\implies

3^{x}*\frac{2}{3}=18. 3

x32=18

3x=18 32\implies

3^{x}=18*\frac{3}{2} 3

{x=18∗ {23}

{3x=27\implies 3^{x}=273 }

{x=27)

{3x=33\implies }

{3^{x}=3^{3}3 }

{x=3 3}

{x=3\implies x=3x=3}

note={2x=23=8\ \{2^{x}=2^{3}=8}∴

2 x=2 3=8}

hence proved

...hope it helps:--

T!—!ANKS!!!