Question

4^x -4^x-1 =24 find x​

Answer 1

$\huge\star{\mathfrak{\underline{\red{QueStion}}}}$

$\large\tt\ 4^x \: - \: 4^{x \: - \: 1} \: = \: 24$

$\huge\star{\mathfrak{\underline{\red{AnSwEr}}}}$

◖Step - by - step - explanation ;

$\large\leadsto\tt\ 4^x \: - \: 4^{x \: - \: 1} \: = \: 24$

$\large\leadsto\tt\ 4^x \: - \: 4^x \times\ 4^{-1} \: = \: 24$

◖Taking $\tt\ 4^x$ common;

$\large\leadsto\tt\ 4^x ( 1 \: - 4^{-1} ) \: = \: 24$

$\large\leadsto\tt\ 4^x ( 1 \: - \: \frac{1}{4} ) \: = \: 24$

$\large\leadsto\tt\ 4^x ( \frac{4 -3}{4} ) \: = \: 24$

$\large\leadsto\tt\ 4^x ( \frac{3}{4} ) \: = \: 24$

$\large\leadsto\tt\ 4^x \: = \: \frac{ 24 \times\ 4 }{3}$

$\large\leadsto\tt\ 4^x \: = \: 32$

◖Now $\tt\ 4^x \: = \: 2^{2x}$ and $\tt\ 32 \: = \: 2^5$

❖So consitute it ;

$\large\leadsto\tt\ 2^{2x} \: = \: 2^5$

◖Comparing power both sides ;

$\large\leadsto\tt\ 2x \: = \: 5$

$\large\leadsto\tt\ x \: = \: \frac{5}{2}$

Answer 2

$\huge\star{\bf{\underline{\green{AnSwEr:-}}}}$

Step - by - step - explanation :-

$\large\to\sf\ 4^x \: - \: 4^{x \: - \: 1} \: = \: 24$

$\large\to\sf\ 4^x \: - \: 4^x \times\ 4^{-1} \: = \: 24$

$\large\to\sf\ 4^x ( 1 \: - 4^{-1} ) \: = \: 24$

$\large\to\sf\ 4^x ( 1 \: - \: \frac{1}{4} ) \: = \: 24$

$\large\to\sf\ 4^x ( \frac{4 -3}{4} ) \: = \: 24$

$\large\to\sf\ 4^x ( \frac{3}{4} ) \: = \: 24$

$\large\to\sf\ 4^x \: = \: \frac{ 24 \times\ 4 }{3}$

$\large\to\sf\ 4^x \: = \: 32$

$\large\to\sf\ 2^{2x} \: = \: 2^5$

•Comparing power both sides ;

$\large\to\sf\ 2x \: = \: 5$

$\large\to\sf\ x \: = \: \frac{5}{2}$