Question

8^x+1=2^x+3 find the value of x

Answer 1

GIVEN :–

$\\ \implies{ \bold{ {8}^{x + 1} = {2}^{x + 3}}}$

TO FIND :–

• Value of 'x' = ?

SOLUTION :–

$\\ \implies{ \bold{ {8}^{x + 1} = {2}^{x + 3}}}$

• We know that –

$\\ \: \: {\huge{.}} \: \: { \bold{ {2}^{0} = 1 }}$

$\\ \: \: {\huge{.}} \: \: { \bold{ {2}^{1} = 2 }}$

$\\ \: \: {\huge{.}} \: \: { \bold{ {2}^{2} = 4 }}$

$\\ \: \: {\huge{.}} \: \: { \bold{ {2}^{3} = 8 }}$

• So that , We can write this as –

$\\ \implies{ \bold{ { ({2}^{3} )}^{x + 1} = {2}^{x + 3}}}$

• Using identity –

$\\ \implies{ \bold{ { ({a}^{b} )}^{c} = {a}^{bc}}}$

$\\ \implies{ \bold{ { (2)}^{3(x + 1)} = {2}^{x + 3}}}$

$\\ \implies{ \bold{ { (2)}^{(3x +3)} = {2}^{x + 3}}}$

• Now Let's compare –

$\\ \implies{ \bold{3x +3 = x + 3}}$

$\\ \implies{ \bold{3x - x = 3 - 3}}$

$\\ \implies{ \bold{2x = 0}}$

$\\ \implies \large{ \boxed{ \bold{x = 0}}}$

$\\ \rule{220}{2}$