Question

Find the value of x if
$({4}^{2x} + 10) \div 2 = 37$
​

Answer 1

$\huge \star\underline {\underline\blue {\mathfrak {ᴀɴsᴡᴇʀ}}} \star$

Given:

$( {4}^{2x} + 10) \div 2 = 37$

To Find:

Value of ${x}$

Solution:

We know that, $( {4}^{2x} + 10) \div 2 = 37$

So,

➩ ${4}^{2x} + 10 = (37 \times 2)$

➩ ${4}^{2x} + 10 = 74$

➩ ${4}^{2x} = 74 - 10$

➩ ${4}^{2x} = 64$

➩ ${4}^{2x} = {4}^{3}$

Taking log on both sides,

➩ $(2x) \: log(4) = 3 \: log(4)$

➩ $2x = 3$

$\large\boxed{x = \frac{3}{2} }$

$\tt\pink{@ChocolateWingz❤~}$

Answer 2

$\huge \star\underline {\underline\pink{\mathfrak {ᴀɴsᴡᴇʀ}}} \star$

Given:

• $( {4}^{2x} + 10) \div 2 = 37$

To Find:

• Value of ${x}$

Solution:

We know that, $( {4}^{2x} + 10) \div 2 = 37$

So,

➩ ${4}^{2x} + 10 = (37 \times 2)$

➩ ${4}^{2x} + 10 = 74$

➩ ${4}^{2x} = 74 - 10$

➩ ${4}^{2x} = 64$

➩ ${4}^{2x} = {4}^{3}$

Taking log on both sides,

➩ $(2x) \: log(4) = 3 \: log(4)$

➩ $2x = 3$

$\large\boxed{x = \frac{3}{2} }$