If 2^{x-2} cdot 3^{2x-6} = 36,then find x. | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given equation: $2^{x-2} \cdot 3^{2x-6} = 36$We know that $36 = 6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2$.So,the equation becomes: $2^{x-2} \cdot 3^{2x

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(C) Given equation: $2^{x-2} \cdot 3^{2x-6} = 36$We know that $36 = 6^2 = (2 \cdot 3)^2 = 2^2 \cdot 3^2$.So,the equation becomes: $2^{x-2} \cdot 3^{2x-6} = 2^2 \cdot 3^2$.By comparing the powers of $2$ and $3$ on both sides:For base $2$: $x - 2 = 2 \implies x = 4$.For base $3$: $2x - 6 = 2 \implies 2x = 8 \implies x = 4$.Since both conditions yield $x = 4$,the value of $x$ is $4$.

If $2^{x-2} \cdot 3^{2x-6} = 36$,then find $x$.

Similar Questions

Simplify: $2^{-3} + (0.01)^{-\frac{1}{2}} - (27)^{\frac{2}{3}}$ (in $.125$)

Find the value of $\left(\frac{125}{64}\right)^{-\frac{2}{3}}$.

Which of the following is not equal to $\left[\left(\frac{5}{6}\right)^{\frac{1}{5}}\right]^{-\frac{1}{6}}?$

Find the value of $625^{\frac{3}{4}}$.

Simplify:
$(i)$ $2^{\frac{2}{3}} \cdot 2^{\frac{1}{3}}$
$(ii)$ $\left(3^{\frac{1}{5}}\right)^{4}$
$(iii)$ $\frac{7^{\frac{1}{5}}}{7^{\frac{1}{3}}}$
$(iv)$ $13^{\frac{1}{5}} \cdot 17^{\frac{1}{5}}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module