Question

find the value of x​

Answer 1

the value of x =19 is the answer of your question

Answer 2

Answer:

$\boxed{\underline{\Huge{\mathtt{x=\frac{5}{2}}}}}$

Step-by-step explanation:

Question:

$4^x-4^{x-1}=24, \:\:\:\:\:\text{Find the value of x}$

Solution:

$4^x-4^{x-1}=24\\\implies 4^x-4^x \times 4^{-1}=24\:\:\: \text{...[Taking 4}^x \text{common.]}\\\implies 4^x[1 - 4^{-1}]=24\\\\\implies 4^x[1 - \frac{1}{4}] = 24\\\\\implies 4^x[\frac{3}{4}] = 24\\\\\implies 4^x = 24 \times \frac{4}{3}=32\\\\\implies 2^{2x}=2^5 \:\:\:\:\:\:\:\:\:\:\:\:\:\:[4=2^2 \text{ and } 32=2^5]\\\implies 2x = 5 \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \text{ [By comparing.]}\\\implies x = \bold{\frac{5}{2}}$