Question

Solve the following equations for x: 2^x+1=4^x-3

Answer 1

Step-by-step explanation:

Given,

$2 {}^{x} + 1 = 4 {}^{x} - 3$

Now,

4^x can also be written as 2^2x

$\implies \: 2 {}^{x} + 1 = 2 {}^{2x} - 3$

On transposing,

$\implies \: 2 {}^{x} = 2 {}^{2x} - 4$

→ -4 can also be written as -2²

$\implies \: 2 {}^{x} = 2 {}^{2x} - 2 {}^{2}$

As,all the base numbers are same.

$\implies \: x = 2x - 2 \\ \\ \implies \: - x = - 2 \\ \\ \implies \: \boxed{x = 2}$

The value of x is 2

Answer 2

ans= 2

2^x + 1 = 4^x - 3

4^x can be written as 2^2x ....

so ..

2^x + 1 = 2^2x - 3

as the variables r same so we will directly solve the exponents...

x = 2x

2x/x = 2

so....x = 2