Question

Solve the equation: 2^x-3 = 4^x-1​

Answer 1

Answer:

x^4 - 4x^3 + 5x^2 + 2x - 8 =0

Answer 2

Answer~

$: \longrightarrow 2^{x-3} = 4^{x-1}$

$\blue: \red \longrightarrow \ \: : 2^{x-3 }= 2^{2 \times (x-1)}$

$\blue : \ \red \longrightarrow \ \: 2^{x-3 }= 2^{2x-2}$

$\orange : \green \longrightarrow \: x - 3 = 2x - 2$

$\orange : \green \longrightarrow \: x - 2x = - 2 + 3$

$\huge \orange : \green \longrightarrow \: { \huge \boxed {x = - 1}}$

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Verification:-

$: \red \longrightarrow 2^{x-3 }= 4^{x-1}$

$: \red \longrightarrow \: 2^ {- 1-3} = 4^{-1 - 1}$

$: \red \longrightarrow \: - 2 = - 2$

$\bigstar \bold \green {Here \: LHS = RHS}$

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