Question

(3/4)6×(16×9)5=(4/3)
$x \times 2$


​

Answer 1

Answer:

3÷4×6×16×9×5

0.75×6×16×9×5

0.75×96×5

72×5

360

Answer 2

$$\begin{lgathered}\\ \implies{ \bold{ { \left( \frac{3}{6} \right) }^{6} \times { \left( \frac{16}{9} \right) }^{5} = \left( \dfrac{4}{3} \right)^{x - 3} }} \\\end{lgathered}$$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$$\begin{lgathered}\\ \implies{ \bold{ { \left( \dfrac{3}{6} \right) }^{6} \times { \left( \dfrac{16}{9} \right) }^{5} = \left( \dfrac{4}{3} \right)^{x - 3} }} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies{ \bold{ { \left( \dfrac{1}{2} \right) }^{6} \times { \left( \dfrac{16}{9} \right) }^{5} = \left( \dfrac{4}{3} \right)^{x - 3} }} \\\end{lgathered}$$

• We should write this as –

$$\begin{lgathered}\\ \implies{ \bold{ { \left( \dfrac{1}{2} \right) }^{6} \times { \left( \dfrac{ {2}^{4} }{ {3}^{2} } \right) }^{5} = \left( \dfrac{4}{3} \right)^{x - 3} }} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies{ \bold{ { \left( \dfrac{1}{2} \right) }^{6} \times { \left( \dfrac{ {2}^{20} }{ {3}^{10} } \right) } = \left( \dfrac{4}{3} \right)^{x - 3} }} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies{ \bold{ { \left( \dfrac{ {2}^{20 - 6} }{ {3}^{10} } \right) } = \left( \dfrac{4}{3} \right)^{x - 3} }} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies{ \bold{ { \left( \dfrac{ {2}^{14} }{ {3}^{10} } \right) } = \left( \dfrac{4}{3} \right)^{x - 3} }} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies{ \bold{ { \left( \dfrac{ {4}^{7} }{ {3}^{10} } \right) } = \left( \dfrac{4}{3} \right)^{x - 3} }} \\\end{lgathered}$$

• Let's take log on both sides –

$$\begin{lgathered}\\ \implies{ \bold{ {log{ \left( \dfrac{ {4}^{7} }{ {3}^{10} } \right) }} =(x - 3) log{ \left( \dfrac{4}{3} \right) }}} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies{ \bold{ \dfrac{ {log{ \left( \dfrac{ {4}^{7} }{ {3}^{10} } \right) }}}{log{ \left( \dfrac{4}{3} \right) }} =(x - 3) }} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies{ \bold{log{ \left( \dfrac{ {4}^{7} }{ {3}^{10} } - \dfrac{4}{3} \right)} =(x - 3) }} \\\end{lgathered}$$

$$\begin{lgathered}\\ \implies \large{ \boxed{ \bold{x = 3 + log{ \left( \dfrac{ {4}^{7} }{ {3}^{10} } - \dfrac{4}{3} \right)}}}} \\\end{lgathered}$$