Question

find the value of x in (3^33+3^33+3^33)(2^33+2^33)=6^x​

Answer 1

Question:-

find the value of x in (3^33+3^33+3^33)(2^33+2^33)=6^x

Solution:-

$\qquad\qquad\displaystyle \bull \hookrightarrow (3^{33}+3^{33}+3^{33})(2^{33}+2^{33})=6^x$

$\qquad\qquad\displaystyle \bull \hookrightarrow 3^{(33+33+33)}×2^{(33+33)}=6^x$

$\qquad\qquad\displaystyle \bull \hookrightarrow 3^{99}×2^{66}=6^x$

$\qquad\qquad\displaystyle \bull \hookrightarrow 3×2^{(99×66)}=6^x$

$\qquad\qquad\displaystyle \bull \hookrightarrow 6^{99×66}=6^x$

$\qquad\qquad\displaystyle \bull \hookrightarrow x=6534$

$\therefore \sf x=6534$

Knowledge booster:-

$\bf{\dag}\bf {\clubsuit}\bf {\maltese}\:\:\underline{\text{Law of Exponents }}\bf{\maltese}\bf {\clubsuit}\bf{\dag}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}$