Question

4^x-4^x-1 = 24 then find the value of x​

Answer 1

Answer:

$\boxed{\bf x=2.5}$

Step-by-step explanation:

The given equation is as follows:

$\boxed{4^{x}-4^{x-1}=24}$

Solve the above equation as shown below:

$\begin{aligned}4^{x}-4^{x-1}&=24\\4^{x}-\dfrac{4^{x}}{4}&=24\\4^{x}\left(1-\dfrac{1}{4}\right)=24\\4^{x}\cdot \dfrac{3}{4}=24\\4^{x}=32\\2^{2x}=2^{5}\\2x&=5\\x&=\dfrac{5}{2}\\x&=2.5\end{aligned}$

Therefore, the value of $x$ is $\boxed{\bf 2.5}$.