Question

if (3/4)^6 * (16/9)^5 =(4/3)^x+2, find the value of x

Answer 1

$\displaystyle \sf{ { \bigg( \frac{3}{4} \bigg)}^{6} \times { \bigg( \frac{16}{9} \bigg)}^{5} = { \bigg( \frac{4}{3} \bigg)}^{x + 2} } \: then \: \: x =2$

Given :

$\displaystyle \sf{ { \bigg( \frac{3}{4} \bigg)}^{6} \times { \bigg( \frac{16}{9} \bigg)}^{5} = { \bigg( \frac{4}{3} \bigg)}^{x + 2} }$

To find : The value of x

Solution :

$\displaystyle \sf{ { \bigg( \frac{3}{4} \bigg)}^{6} \times { \bigg( \frac{16}{9} \bigg)}^{5} = { \bigg( \frac{4}{3} \bigg)}^{x + 2} }$

$\displaystyle \sf{ \implies \bigg({{ \bigg( \frac{4}{3} \bigg)}^{ - 1} \bigg) }^{ 6} \times { \bigg({ \bigg( \frac{4}{3} \bigg) }^{2} \bigg) }^{5} = { \bigg( \frac{4}{3} \bigg)}^{x + 2} }$

$\displaystyle \sf{ \implies {{ \bigg( \frac{4}{3} } \bigg) }^{ - 6} \times { \bigg({ \frac{4}{3} \bigg) } }^{10} = { \bigg( \frac{4}{3} \bigg)}^{x + 2} }$

$\displaystyle \sf{ \implies {{ \bigg( \frac{4}{3} } \bigg) }^{ 10 - 6} = { \bigg( \frac{4}{3} \bigg)}^{x + 2} }$

$\displaystyle \sf{ \implies {{ \bigg( \frac{4}{3} } \bigg) }^{ 4} = { \bigg( \frac{4}{3} \bigg)}^{x + 2} }$

$\displaystyle \sf{ \implies {{ \bigg( \frac{4}{3} } \bigg) }^{ x + 2} = { \bigg( \frac{4}{3} \bigg)}^{4} }$

$\displaystyle \sf{ \implies x + 2 = 4 }$

$\displaystyle \sf{ \implies x= 2}$

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Answer 2

Answer:

2

Step-by-step explanation:

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