Step-by-step explanation:
hence the value of x=11 hope it helps
PLEASE MARK ME THE BRAINLIEST
[tex] \qquad \qquad \: \begin{gathered}\boxed{\begin {aligned}\sf \large value \: of \: x \: = 11 \\ \\ \sf value \large \: of \: y \: = 19 \end{aligned}} \\ \\ \end{gathered}[/tex]
Given :
[tex] \qquad \quad \sf {(3)}^{x} \: = \: 9 \: \times \: {(3)}^{9} \\ \\ \qquad \quad \sf8 \: \times \: {(2)}^{y} \: = \: {(4)}^{x} \\ \\ [/tex]
To find :
we have to find out the values of x and y .
Solution :
Approach :
For finding value of x :-
[tex] \qquad \sf \: {(3)}^{x} = 9 \times {(3)}^{9} \\ \\ \qquad \sf \: {(3)}^{x} = {(3)}^{2} \times {(3)}^{9} \\ \\ \qquad \sf \: {(3)}^{x} = {(3)}^{2 + 9} \\ \\ \qquad \sf \: {(3)}^{x} = {(3)}^{11} \\ \\ \therefore \qquad \boxed{\sf \:x = 11} \\ [/tex]
Now, we have the value of x = 11 .
to find out the value of y we will put this value in second expression.
[tex] \qquad \sf \:8 \times {(2)}^{y} = 4x \\ \\ \qquad \sf \:8 \times {(2)}^{y} = {(4)}^{11} \\ \\ \qquad \sf \: {(2)}^{y} = \dfrac{ {(4)}^{11} }{8} \\ \\ \qquad \sf \: {(2)}^{y} = \frac{ {(2 \times 2)}^{11} }{2 \times 2 \times 2} \\ \\ \qquad \sf \: {(2)}^{y} = \frac{ { \big( {2}^{2} \big) }^{11} }{ {2}^{3} } \\ \\ \qquad \sf \: {(2)}^{y} = \frac{ {(2)}^{22} }{ {2}^{3} } \\ \\ \qquad \sf \: {(2)}^{y} = {(2)}^{22} \times {(2)}^{ - 3} \\ \\ \qquad \sf \: {(2)}^{y} = {(2)}^{22 - 3} \\ \\ \qquad \sf \: {(2)}^{y} = {2}^{19} \\ \\ \therefore\qquad \sf \: y= \boxed { \sf 19} \\ \\ [/tex]
Hence, we have the value of y = 19 .
conclusively,
[tex]\rule{190pt}{2pt} \\ [/tex]
ADDITIONAL INFORMATION :
[tex]\begin{gathered}\boxed{\begin {aligned}\sf {(a)}^{n} \times {(a)}^{m} = {(a)}^{ n+ m} \\ \\ \sf {(a)}^{n} \div {(a)}^{m} = {(a)}^{n - m} \\ \\ \sf {( {a}^{n}) }^{m} \: \: \: \: = \: \: \: \: \: {(a)}^{n \times m} \\ \\ \sf {(a)}^{0} \: \: \: \: \: = \: \: \: \: \: \: \: 1 \: \: \: \: \: \: \: \: \\ \end{aligned}} \\ \\ \end{gathered}[/tex]
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Answers & Comments
Step-by-step explanation:
hence the value of x=11 hope it helps
PLEASE MARK ME THE BRAINLIEST
Verified answer
[tex] \qquad \qquad \: \begin{gathered}\boxed{\begin {aligned}\sf \large value \: of \: x \: = 11 \\ \\ \sf value \large \: of \: y \: = 19 \end{aligned}} \\ \\ \end{gathered}[/tex]
Step-by-step explanation:
Given :
[tex] \qquad \quad \sf {(3)}^{x} \: = \: 9 \: \times \: {(3)}^{9} \\ \\ \qquad \quad \sf8 \: \times \: {(2)}^{y} \: = \: {(4)}^{x} \\ \\ [/tex]
To find :
we have to find out the values of x and y .
Solution :
Approach :
For finding value of x :-
[tex] \qquad \sf \: {(3)}^{x} = 9 \times {(3)}^{9} \\ \\ \qquad \sf \: {(3)}^{x} = {(3)}^{2} \times {(3)}^{9} \\ \\ \qquad \sf \: {(3)}^{x} = {(3)}^{2 + 9} \\ \\ \qquad \sf \: {(3)}^{x} = {(3)}^{11} \\ \\ \therefore \qquad \boxed{\sf \:x = 11} \\ [/tex]
Now, we have the value of x = 11 .
to find out the value of y we will put this value in second expression.
[tex] \qquad \sf \:8 \times {(2)}^{y} = 4x \\ \\ \qquad \sf \:8 \times {(2)}^{y} = {(4)}^{11} \\ \\ \qquad \sf \: {(2)}^{y} = \dfrac{ {(4)}^{11} }{8} \\ \\ \qquad \sf \: {(2)}^{y} = \frac{ {(2 \times 2)}^{11} }{2 \times 2 \times 2} \\ \\ \qquad \sf \: {(2)}^{y} = \frac{ { \big( {2}^{2} \big) }^{11} }{ {2}^{3} } \\ \\ \qquad \sf \: {(2)}^{y} = \frac{ {(2)}^{22} }{ {2}^{3} } \\ \\ \qquad \sf \: {(2)}^{y} = {(2)}^{22} \times {(2)}^{ - 3} \\ \\ \qquad \sf \: {(2)}^{y} = {(2)}^{22 - 3} \\ \\ \qquad \sf \: {(2)}^{y} = {2}^{19} \\ \\ \therefore\qquad \sf \: y= \boxed { \sf 19} \\ \\ [/tex]
Hence, we have the value of y = 19 .
conclusively,
[tex]\rule{190pt}{2pt} \\ [/tex]
ADDITIONAL INFORMATION :
[tex]\begin{gathered}\boxed{\begin {aligned}\sf {(a)}^{n} \times {(a)}^{m} = {(a)}^{ n+ m} \\ \\ \sf {(a)}^{n} \div {(a)}^{m} = {(a)}^{n - m} \\ \\ \sf {( {a}^{n}) }^{m} \: \: \: \: = \: \: \: \: \: {(a)}^{n \times m} \\ \\ \sf {(a)}^{0} \: \: \: \: \: = \: \: \: \: \: \: \: 1 \: \: \: \: \: \: \: \: \\ \end{aligned}} \\ \\ \end{gathered}[/tex]