Question

find x if $\frac{2^{2x-2}}{8}= 32$

Answer 1

Answer:

X = 5

Step-by-step explanation:

• We are asked to find the value of x in $\frac{2^{2x-2}}{8}= 32$
• We will use the exponential rules to work out this amazing problem.
• We will also have to change few digits in the power of 2 such as 8 and 32

$\hookrightarrow$ Let's proceed !!

$\frac{2^{2x-2}}{8}= 32$

$\frac{ {2}^{(2x - 2)} }{ {2}^{3} } = 32$

{ $\because$ 8 = ${2}^{3}$ }

Now, let's use the exponential rule:

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

We get

${2}^{(2x - 2) - 3} = 32$

Now,

{ 32 = ${2}^{5}$ }

$\therefore$ we get

${2}^{2x - 5} = {2}^{5}$

Since, bases are same at both sides, we have

2x - 5 = 5

2x = 10

$x \: = \frac{10}{2}$

$\therefore$ x = 5